[Introduction] - Groups of Genus: 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24

Congruence Subgroups of PSL(2,Z) of Genus 1

Groups of Level: 6 7 8 9 10 11 12 14 15 16 17 18 19 20 21 22 24 26 27 28 30 32 33 36 39 40 42 49 52
 
 
^ Level 6 Name Index  con   len   c2   c3  > SL(2,Z/6Z) Matrix Generators
  6A1 Γ' 6 1 1 0 0 [ 1, 3, 3, 4 ] , [ 3, 2, 4, 3 ] , [ 4, 3, 3, 1 ] , [ 5, 0, 0, 5 ] , [ 5, 4, 4, 1 ]
  6B1 12 1 3 0 0 [ 1, 5, 5, 2 ] , [ 4, 3, 3, 1 ] , [ 5, 0, 0, 5 ] , [ 5, 4, 4, 1 ]
  6C1 18 1 1 0 0 [ 1, 4, 4, 5 ] , [ 3, 4, 2, 3 ] , [ 5, 0, 0, 5 ]
  6D1 24 1 1 0 0 [ 4, 3, 3, 1 ] , [ 5, 0, 0, 5 ]
  6E1 36 1 3 0 0 [ 5, 0, 0, 5 ] , [ 5, 4, 4, 1 ]
  6F1 Γ(6) 72 1 1 0 0 [ 5, 0, 0, 5 ]
^ Level 7 Name Index  con   len   c2   c3  > SL(2,Z/7Z) Matrix Generators
  7A1 42 1 21 2 0 [ 2, 5, 6, 5 ] , [ 6, 0, 0, 6 ] , [ 6, 3, 5, 5 ]
  7B1 56 1 28 0 2 [ 4, 0, 2, 2 ] , [ 6, 0, 0, 6 ]
  7C1 84 1 21 4 0 [ 0, 3, 2, 0 ] , [ 6, 0, 0, 6 ]
^ Level 8 Name Index  con   len   c2   c3  > SL(2,Z/8Z) Matrix Generators
  8A1 12 1 3 0 0 [ 3, 6, 6, 7 ] , [ 4, 5, 3, 0 ] , [ 5, 0, 0, 5 ] , [ 5, 4, 4, 5 ] , [ 7, 4, 4, 7 ] , [ 7, 6, 6, 3 ]
  8B1 24 1 3 0 0 [ 1, 4, 0, 1 ] , [ 1, 6, 4, 1 ] , [ 3, 2, 4, 3 ] , [ 5, 4, 0, 5 ] , [ 5, 6, 4, 5 ]
  8C1 24 1 6 0 0 [ 1, 4, 4, 1 ] , [ 4, 1, 7, 0 ] , [ 5, 0, 0, 5 ] , [ 7, 4, 4, 7 ]
  8D1 24 1 12 2 0 [ 1, 4, 4, 1 ] , [ 4, 1, 7, 0 ] , [ 5, 0, 4, 5 ] , [ 7, 4, 4, 7 ]
  8E1 32 1 16 0 2 [ 2, 3, 3, 5 ] , [ 3, 0, 0, 3 ] , [ 7, 0, 0, 7 ]
  8F1 48 1 3 0 0 [ 3, 0, 0, 3 ] , [ 7, 0, 0, 7 ] , [ 7, 4, 4, 7 ]
  8G1 48 1 6 0 0 [ 1, 4, 0, 1 ] , [ 3, 2, 4, 3 ] , [ 7, 4, 0, 7 ]
  8H1 48 1 12 4 0 [ 0, 3, 5, 0 ] , [ 1, 4, 4, 1 ] , [ 7, 4, 4, 7 ]
  8I1 48 1 12 4 0 [ 0, 1, 7, 0 ] , [ 0, 5, 3, 0 ] , [ 7, 0, 0, 7 ]
  8J1 64 1 16 0 4 [ 2, 3, 3, 5 ] , [ 7, 0, 0, 7 ]
  8K1 96 1 3 0 0 [ 5, 4, 4, 5 ] , [ 7, 0, 0, 7 ]
^ Level 9 Name Index  con   len   c2   c3  > SL(2,Z/9Z) Matrix Generators
  9A1 12 1 4 0 0 [ 4, 0, 6, 7 ] , [ 4, 6, 5, 1 ] , [ 7, 0, 6, 4 ] , [ 8, 0, 0, 8 ]
  9B1 18 2 9 2 0 [ 1, 7, 1, 8 ] , [ 4, 6, 6, 7 ] , [ 5, 3, 3, 2 ] , [ 7, 0, 0, 4 ]
  9C1 36 1 4 0 0 [ 1, 0, 6, 1 ] , [ 4, 0, 3, 7 ] , [ 8, 0, 0, 8 ]
  9D1 36 1 12 0 0 [ 1, 0, 6, 1 ] , [ 7, 6, 5, 7 ] , [ 8, 0, 0, 8 ]
  9E1 54 1 18 6 0 [ 0, 1, 8, 0 ] , [ 7, 0, 0, 4 ] , [ 8, 0, 0, 8 ]
  9F1 54 2 9 6 0 [ 0, 1, 8, 0 ] , [ 5, 3, 3, 2 ] , [ 7, 3, 3, 4 ]
  9G1 81 1 27 9 0 [ 1, 5, 5, 8 ] , [ 4, 1, 1, 5 ] , [ 5, 8, 8, 4 ] , [ 8, 0, 0, 8 ]
  9H1 108 1 4 0 0 [ 1, 0, 3, 1 ] , [ 8, 0, 0, 8 ]
^ Level 10 Name Index  con   len   c2   c3  > SL(2,Z/10Z) Matrix Generators
  10A1 12 1 6 0 0 [ 6, 5, 5, 1 ] , [ 7, 8, 8, 5 ] , [ 9, 0, 0, 9 ] , [ 9, 6, 8, 1 ]
  10B1 15 1 15 1 0 [ 1, 0, 5, 1 ] , [ 1, 4, 8, 3 ] , [ 1, 8, 6, 9 ] , [ 3, 0, 8, 7 ] , [ 9, 0, 0, 9 ]
  10C1 20 1 10 0 2 [ 1, 5, 5, 6 ] , [ 7, 4, 0, 3 ] , [ 9, 0, 0, 9 ] , [ 9, 8, 8, 5 ]
  10D1 24 1 6 0 0 [ 3, 6, 6, 9 ] , [ 6, 5, 5, 1 ] , [ 9, 0, 0, 9 ]
  10E1 30 1 15 4 0 [ 3, 4, 5, 7 ] , [ 6, 5, 5, 1 ] , [ 7, 0, 2, 3 ] , [ 9, 0, 0, 9 ]
  10F1 30 1 30 2 0 [ 1, 0, 5, 1 ] , [ 7, 4, 5, 3 ] , [ 9, 0, 0, 9 ] , [ 9, 8, 8, 5 ]
  10G1 36 1 6 0 0 [ 5, 2, 2, 7 ] , [ 9, 0, 0, 9 ] , [ 9, 8, 6, 1 ]
  10H1 40 1 10 0 4 [ 6, 5, 5, 1 ] , [ 9, 0, 0, 9 ] , [ 9, 8, 8, 5 ]
  10I1 45 1 15 3 0 [ 1, 0, 5, 1 ] , [ 3, 4, 5, 7 ] , [ 7, 0, 2, 3 ] , [ 9, 0, 0, 9 ]
  10J1 60 1 60 4 3 [ 5, 4, 1, 5 ] , [ 9, 0, 0, 9 ] , [ 9, 3, 3, 0 ]
  10K1 72 1 6 0 0 [ 3, 6, 6, 9 ] , [ 5, 2, 2, 7 ] , [ 9, 0, 0, 9 ]
^ Level 11 Name Index  con   len   c2   c3  > SL(2,Z/11Z) Matrix Generators
  11A1 Γ0(11) 12 1 12 0 0 [ 7, 0, 7, 8 ] , [ 8, 1, 6, 5 ] , [ 10, 0, 0, 10 ]
  11B1 55 1 55 3 4 [ 3, 1, 1, 8 ] , [ 3, 5, 3, 9 ] , [ 6, 7, 1, 5 ] , [ 10, 0, 0, 10 ]
  11C1 55 1 55 7 1 [ 0, 10, 1, 0 ] , [ 1, 8, 8, 10 ] , [ 3, 9, 9, 9 ] , [ 10, 0, 0, 10 ]
  11D1 Γ1(11) 60 1 12 0 0 [ 4, 2, 1, 9 ] , [ 10, 0, 0, 10 ]
^ Level 12 Name Index  con   len   c2   c3  > SL(2,Z/12Z) Matrix Generators
  12A1 16 1 16 0 1 [ 1, 0, 8, 1 ] , [ 1, 9, 9, 10 ] , [ 4, 9, 3, 4 ] , [ 5, 0, 0, 5 ] , [ 5, 0, 4, 5 ] , [ 7, 0, 0, 7 ]
  12B1 18 1 3 0 0 [ 1, 4, 4, 5 ] , [ 1, 6, 6, 1 ] , [ 4, 3, 9, 10 ] , [ 5, 0, 0, 5 ] , [ 7, 0, 0, 7 ] , [ 7, 6, 6, 7 ] , [ 9, 4, 8, 9 ] , [ 10, 3, 9, 4 ]
  12C1 18 1 9 2 0 [ 0, 7, 5, 6 ] , [ 1, 6, 6, 1 ] , [ 4, 3, 9, 4 ] , [ 5, 0, 0, 5 ] , [ 5, 4, 4, 1 ] , [ 7, 0, 0, 7 ] , [ 7, 6, 6, 7 ] , [ 9, 4, 2, 9 ]
  12D1 24 1 6 4 0 [ 1, 6, 6, 1 ] , [ 1, 8, 11, 5 ] , [ 5, 0, 6, 5 ] , [ 7, 2, 5, 5 ] , [ 7, 3, 9, 4 ] , [ 7, 6, 0, 7 ] , [ 11, 0, 0, 11 ]
  12E1 24 1 8 0 3 [ 1, 8, 8, 5 ] , [ 1, 9, 5, 10 ] , [ 5, 0, 0, 5 ] , [ 7, 0, 0, 7 ] , [ 9, 8, 4, 9 ] , [ 10, 11, 3, 1 ] , [ 11, 0, 0, 11 ]
  12F1 24 1 12 0 0 [ 1, 0, 6, 1 ] , [ 3, 2, 1, 5 ] , [ 7, 0, 6, 7 ] , [ 9, 4, 8, 1 ] , [ 9, 8, 4, 5 ] , [ 11, 4, 8, 3 ] , [ 11, 10, 5, 9 ]
  12G1 24 1 12 4 0 [ 4, 9, 3, 4 ] , [ 5, 0, 0, 5 ] , [ 7, 0, 0, 7 ] , [ 9, 4, 8, 9 ] , [ 9, 8, 4, 9 ] , [ 10, 3, 3, 1 ] , [ 11, 0, 0, 11 ]
  12H1 24 1 24 0 3 [ 1, 2, 2, 5 ] , [ 3, 8, 10, 3 ] , [ 5, 0, 0, 5 ] , [ 5, 3, 1, 8 ] , [ 7, 2, 2, 11 ] , [ 8, 5, 7, 3 ] , [ 9, 4, 2, 9 ]
  12I1 32 1 16 0 2 [ 1, 0, 8, 1 ] , [ 5, 0, 0, 5 ] , [ 5, 0, 4, 5 ] , [ 7, 0, 0, 7 ] , [ 10, 3, 3, 1 ] , [ 11, 0, 8, 11 ]
  12J1 36 1 6 6 0 [ 4, 9, 3, 4 ] , [ 5, 0, 0, 5 ] , [ 5, 4, 4, 1 ] , [ 7, 0, 0, 7 ] , [ 9, 4, 8, 9 ] , [ 9, 8, 4, 9 ] , [ 11, 0, 0, 11 ]
  12K1 36 1 9 0 0 [ 4, 1, 7, 2 ] , [ 4, 3, 9, 10 ] , [ 4, 9, 3, 10 ] , [ 5, 0, 0, 5 ] , [ 5, 8, 8, 1 ] , [ 7, 0, 0, 7 ] , [ 7, 6, 6, 7 ]
  12L1 36 1 9 4 0 [ 1, 6, 6, 1 ] , [ 5, 0, 0, 5 ] , [ 5, 4, 4, 1 ] , [ 7, 6, 6, 7 ] , [ 7, 8, 8, 11 ] , [ 10, 9, 3, 10 ] , [ 11, 0, 0, 11 ]
  12M1 36 1 18 6 0 [ 5, 0, 0, 5 ] , [ 5, 2, 2, 1 ] , [ 7, 0, 0, 7 ] , [ 8, 5, 11, 4 ] , [ 9, 8, 4, 9 ]
  12N1 36 2 9 4 0 [ 0, 7, 5, 6 ] , [ 1, 6, 6, 1 ] , [ 2, 1, 7, 10 ] , [ 5, 0, 0, 5 ] , [ 5, 8, 2, 1 ] , [ 7, 6, 6, 7 ] , [ 11, 0, 0, 11 ]
  12O1 48 1 8 0 6 [ 1, 6, 6, 1 ] , [ 2, 1, 5, 9 ] , [ 5, 0, 6, 5 ] , [ 7, 6, 0, 7 ] , [ 9, 11, 7, 2 ] , [ 11, 0, 0, 11 ]
  12P1 48 1 12 0 0 [ 1, 8, 4, 9 ] , [ 5, 4, 8, 9 ] , [ 7, 0, 0, 7 ] , [ 9, 8, 4, 5 ] , [ 9, 8, 10, 5 ]
  12Q1 48 1 12 8 0 [ 5, 0, 0, 5 ] , [ 7, 0, 0, 7 ] , [ 8, 1, 7, 4 ] , [ 10, 3, 3, 1 ] , [ 11, 0, 0, 11 ]
  12R1 64 1 16 0 4 [ 1, 0, 4, 1 ] , [ 1, 0, 8, 1 ] , [ 10, 3, 3, 1 ] , [ 11, 0, 4, 11 ]
  12S1 72 1 3 0 0 [ 1, 0, 6, 1 ] , [ 1, 0, 9, 1 ] , [ 5, 0, 0, 5 ] , [ 7, 0, 0, 7 ] , [ 7, 0, 3, 7 ] , [ 7, 0, 6, 7 ] , [ 11, 0, 0, 11 ]
  12T1 72 1 9 8 0 [ 4, 11, 5, 8 ] , [ 5, 0, 0, 5 ] , [ 7, 0, 0, 7 ] , [ 7, 6, 6, 7 ]
  12U1 72 1 18 4 0 [ 0, 7, 5, 0 ] , [ 0, 7, 5, 6 ] , [ 1, 6, 6, 1 ] , [ 11, 0, 0, 11 ] , [ 11, 0, 6, 11 ]
  12V1 96 1 12 0 0 [ 1, 0, 6, 1 ] , [ 5, 4, 8, 9 ] , [ 7, 8, 10, 3 ] , [ 9, 8, 4, 5 ]
^ Level 14 Name Index  con   len   c2   c3  > SL(2,Z/14Z) Matrix Generators
  14A1 14 2 7 0 2 [ 1, 2, 4, 9 ] , [ 5, 8, 2, 9 ] , [ 7, 12, 4, 7 ] , [ 8, 7, 7, 1 ] , [ 11, 12, 0, 9 ] , [ 13, 0, 0, 13 ]
  14B1 21 2 21 3 0 [ 1, 2, 4, 9 ] , [ 1, 7, 0, 1 ] , [ 5, 8, 2, 9 ] , [ 7, 12, 4, 7 ] , [ 11, 12, 0, 9 ] , [ 13, 0, 0, 13 ]
  14C1 Γ0(14) 24 1 24 0 0 [ 1, 0, 7, 1 ] , [ 11, 8, 12, 5 ] , [ 13, 10, 2, 7 ] , [ 13, 12, 12, 9 ]
  14D1 28 2 7 0 4 [ 3, 10, 6, 11 ] , [ 5, 8, 2, 9 ] , [ 7, 10, 2, 13 ] , [ 8, 7, 7, 1 ] , [ 9, 6, 12, 5 ] , [ 13, 0, 0, 13 ]
  14E1 42 1 21 8 0 [ 1, 9, 11, 2 ] , [ 2, 13, 5, 5 ] , [ 6, 3, 11, 8 ] , [ 8, 7, 7, 1 ] , [ 13, 7, 7, 6 ]
  14F1 42 2 42 4 3 [ 0, 3, 9, 13 ] , [ 1, 9, 4, 9 ] , [ 3, 10, 6, 11 ] , [ 5, 8, 2, 9 ] , [ 9, 6, 12, 5 ] , [ 13, 0, 0, 13 ]
  14G1 56 1 28 8 2 [ 1, 7, 7, 8 ] , [ 1, 12, 1, 13 ] , [ 9, 2, 0, 11 ] , [ 13, 0, 0, 13 ]
  14H1 Γ1(14) 72 1 24 0 0 [ 3, 3, 8, 13 ] , [ 5, 6, 2, 11 ] , [ 11, 8, 12, 5 ] , [ 11, 11, 6, 1 ]
^ Level 15 Name Index  con   len   c2   c3  > SL(2,Z/15Z) Matrix Generators
  15A1 15 1 5 3 0 [ 1, 3, 6, 4 ] , [ 1, 9, 3, 13 ] , [ 4, 0, 0, 4 ] , [ 6, 10, 5, 6 ] , [ 11, 0, 0, 11 ] , [ 11, 5, 5, 1 ] , [ 13, 0, 3, 7 ]
  15B1 20 1 20 0 2 [ 4, 0, 0, 4 ] , [ 4, 9, 6, 10 ] , [ 6, 5, 10, 11 ] , [ 7, 0, 9, 13 ] , [ 7, 3, 0, 13 ] , [ 11, 0, 0, 11 ] , [ 11, 10, 5, 6 ]
  15C1 Γ0(15) 24 1 24 0 0 [ 1, 0, 5, 1 ] , [ 1, 0, 10, 1 ] , [ 7, 3, 3, 10 ] , [ 11, 0, 0, 11 ] , [ 14, 0, 0, 14 ] , [ 14, 6, 3, 11 ]
  15D1 30 1 10 6 0 [ 1, 5, 5, 11 ] , [ 4, 0, 0, 4 ] , [ 4, 3, 3, 10 ] , [ 6, 5, 10, 6 ] , [ 7, 9, 0, 13 ] , [ 11, 0, 0, 11 ]
  15E1 36 1 18 4 0 [ 1, 10, 10, 11 ] , [ 2, 0, 12, 8 ] , [ 7, 3, 3, 10 ] , [ 11, 0, 0, 11 ] , [ 14, 0, 0, 14 ]
  15F1 45 1 5 9 0 [ 1, 3, 6, 4 ] , [ 4, 0, 0, 4 ] , [ 6, 5, 10, 6 ] , [ 7, 0, 12, 13 ] , [ 11, 0, 0, 11 ] , [ 11, 10, 10, 1 ]
  15G1 48 1 24 0 0 [ 1, 0, 5, 1 ] , [ 4, 0, 10, 4 ] , [ 7, 3, 3, 10 ] , [ 11, 0, 5, 11 ]
  15H1 72 1 18 8 0 [ 4, 0, 0, 4 ] , [ 5, 12, 12, 2 ] , [ 10, 4, 1, 5 ] , [ 13, 6, 6, 4 ]
  15I1 Γ1(15) 96 1 24 0 0 [ 1, 0, 5, 1 ] , [ 1, 0, 10, 1 ] , [ 8, 12, 7, 5 ] , [ 13, 6, 6, 4 ]
^ Level 16 Name Index  con   len   c2   c3  > SL(2,Z/16Z) Matrix Generators
  16A1 24 1 6 0 0 [ 1, 8, 8, 1 ] , [ 1, 12, 12, 1 ] , [ 5, 4, 12, 13 ] , [ 9, 0, 0, 9 ] , [ 9, 8, 8, 9 ] , [ 11, 2, 14, 7 ] , [ 12, 13, 3, 10 ] , [ 13, 2, 6, 1 ]
  16B1 24 1 6 4 0 [ 1, 8, 8, 1 ] , [ 1, 10, 2, 5 ] , [ 2, 7, 13, 6 ] , [ 4, 1, 15, 12 ] , [ 5, 4, 4, 13 ] , [ 9, 0, 0, 9 ] , [ 9, 8, 8, 9 ] , [ 15, 0, 0, 15 ] , [ 15, 12, 12, 15 ]
  16C1 24 1 12 2 0 [ 1, 8, 8, 1 ] , [ 9, 0, 0, 9 ] , [ 10, 9, 11, 10 ] , [ 12, 3, 5, 4 ] , [ 13, 8, 8, 5 ] , [ 13, 12, 4, 5 ] , [ 15, 8, 8, 15 ]
  16D1 24 1 12 4 0 [ 1, 8, 8, 1 ] , [ 1, 10, 2, 5 ] , [ 2, 7, 13, 14 ] , [ 5, 4, 4, 13 ] , [ 9, 0, 0, 9 ] , [ 9, 8, 8, 9 ] , [ 11, 6, 6, 15 ] , [ 15, 0, 0, 15 ] , [ 15, 12, 4, 15 ]
  16E1 48 1 6 0 0 [ 1, 4, 0, 1 ] , [ 1, 8, 0, 1 ] , [ 3, 14, 8, 11 ] , [ 5, 0, 0, 13 ] , [ 9, 0, 0, 9 ] , [ 9, 6, 8, 9 ] , [ 9, 8, 0, 9 ]
  16F1 48 1 6 8 0 [ 5, 12, 12, 13 ] , [ 7, 12, 12, 7 ] , [ 8, 15, 1, 8 ] , [ 9, 0, 0, 9 ] , [ 9, 8, 8, 9 ] , [ 15, 0, 0, 15 ]
  16G1 48 1 12 0 0 [ 0, 1, 15, 6 ] , [ 1, 8, 8, 1 ] , [ 2, 3, 13, 4 ] , [ 9, 8, 8, 9 ] , [ 13, 6, 10, 1 ] , [ 13, 12, 4, 5 ] , [ 15, 6, 10, 3 ]
  16H1 48 1 12 4 0 [ 3, 8, 0, 11 ] , [ 7, 12, 12, 7 ] , [ 8, 15, 1, 8 ] , [ 9, 0, 0, 9 ] , [ 9, 8, 8, 9 ] , [ 15, 0, 0, 15 ]
  16I1 48 1 12 4 0 [ 3, 8, 8, 11 ] , [ 4, 3, 5, 12 ] , [ 7, 12, 4, 7 ] , [ 9, 0, 0, 9 ] , [ 9, 8, 8, 9 ] , [ 15, 0, 0, 15 ]
  16J1 48 1 12 8 0 [ 1, 8, 8, 1 ] , [ 9, 8, 8, 9 ] , [ 11, 6, 6, 15 ] , [ 11, 14, 14, 15 ] , [ 13, 12, 12, 5 ] , [ 14, 11, 1, 2 ] , [ 15, 0, 0, 15 ] , [ 15, 2, 2, 11 ]
  16K1 48 1 24 2 0 [ 0, 5, 3, 12 ] , [ 1, 0, 8, 1 ] , [ 1, 4, 4, 1 ] , [ 1, 8, 8, 1 ] , [ 9, 8, 4, 9 ] , [ 15, 0, 0, 15 ] , [ 15, 4, 4, 15 ]
  16L1 48 1 24 2 0 [ 0, 5, 3, 12 ] , [ 1, 0, 4, 1 ] , [ 1, 0, 8, 1 ] , [ 1, 4, 4, 1 ] , [ 1, 8, 8, 1 ] , [ 15, 0, 0, 15 ] , [ 15, 4, 4, 15 ]
  16M1 96 1 6 0 0 [ 1, 8, 0, 1 ] , [ 1, 12, 0, 1 ] , [ 9, 12, 0, 9 ] , [ 13, 2, 8, 5 ] , [ 13, 10, 8, 5 ] , [ 15, 4, 0, 15 ]
^ Level 17 Name Index  con   len   c2   c3  > SL(2,Z/17Z) Matrix Generators
  17A1 Γ0(17) 18 1 18 2 0 [ 4, 0, 15, 13 ] , [ 9, 0, 11, 2 ] , [ 11, 0, 5, 14 ] , [ 16, 0, 0, 16 ] , [ 16, 0, 4, 16 ]
  17B1 36 1 18 4 0 [ 1, 0, 8, 1 ] , [ 4, 0, 14, 13 ] , [ 15, 0, 8, 8 ] , [ 16, 0, 0, 16 ]
  17C1 72 1 18 8 0 [ 1, 0, 2, 1 ] , [ 13, 0, 15, 4 ] , [ 16, 0, 0, 16 ]
^ Level 18 Name Index  con   len   c2   c3  > SL(2,Z/18Z) Matrix Generators
  18A1 18 1 9 4 0 [ 1, 9, 9, 10 ] , [ 1, 16, 1, 17 ] , [ 5, 12, 12, 11 ] , [ 7, 0, 0, 13 ] , [ 9, 10, 8, 9 ] , [ 13, 6, 6, 7 ]
  18B1 18 1 18 4 0 [ 1, 16, 1, 17 ] , [ 3, 4, 11, 3 ] , [ 4, 9, 3, 7 ] , [ 7, 3, 3, 4 ] , [ 13, 15, 3, 16 ] , [ 17, 6, 12, 17 ]
  18C1 24 1 4 0 0 [ 1, 9, 9, 10 ] , [ 1, 9, 15, 10 ] , [ 10, 9, 9, 1 ] , [ 13, 0, 0, 7 ] , [ 16, 9, 5, 13 ] , [ 17, 0, 0, 17 ]
  18D1 24 1 8 0 3 [ 1, 0, 6, 1 ] , [ 1, 3, 3, 10 ] , [ 7, 15, 1, 10 ] , [ 13, 0, 12, 7 ] , [ 17, 0, 0, 17 ]
  18E1 27 1 27 5 0 [ 7, 6, 6, 13 ] , [ 11, 10, 4, 7 ] , [ 13, 6, 0, 7 ] , [ 15, 10, 17, 15 ] , [ 15, 14, 16, 9 ] , [ 17, 6, 12, 17 ]
  18F1 36 1 18 4 0 [ 1, 0, 6, 1 ] , [ 1, 9, 9, 10 ] , [ 1, 15, 15, 10 ] , [ 15, 4, 11, 15 ] , [ 17, 12, 6, 17 ]
  18G1 36 1 36 4 0 [ 1, 0, 6, 1 ] , [ 4, 3, 3, 7 ] , [ 4, 15, 15, 7 ] , [ 15, 4, 11, 15 ] , [ 17, 12, 6, 17 ]
  18H1 54 1 27 12 0 [ 0, 1, 17, 0 ] , [ 5, 12, 12, 11 ] , [ 7, 12, 12, 13 ] , [ 10, 7, 1, 8 ] , [ 10, 9, 9, 1 ]
  18I1 54 1 54 2 0 [ 7, 0, 12, 13 ] , [ 7, 6, 3, 13 ] , [ 7, 12, 12, 13 ] , [ 11, 6, 6, 5 ] , [ 17, 16, 4, 7 ]
  18J1 72 1 4 0 0 [ 1, 0, 12, 1 ] , [ 7, 0, 2, 13 ] , [ 13, 0, 0, 7 ] , [ 17, 0, 0, 17 ]
  18K1 72 1 8 0 9 [ 1, 0, 6, 1 ] , [ 7, 0, 6, 13 ] , [ 16, 15, 7, 1 ] , [ 17, 0, 0, 17 ]
^ Level 19 Name Index  con   len   c2   c3  > SL(2,Z/19Z) Matrix Generators
  19A1 Γ0(19) 20 1 20 0 2 [ 0, 18, 1, 1 ] , [ 2, 7, 12, 14 ] , [ 3, 5, 3, 18 ] , [ 18, 0, 0, 18 ]
  19B1 60 1 20 0 6 [ 11, 0, 6, 7 ] , [ 16, 9, 13, 5 ] , [ 18, 0, 0, 18 ]
^ Level 20 Name Index  con   len   c2   c3  > SL(2,Z/20Z) Matrix Generators
  20A1 20 1 20 2 2 [ 1, 5, 5, 6 ] , [ 4, 5, 15, 4 ] , [ 11, 0, 0, 11 ] , [ 13, 4, 0, 17 ] , [ 13, 8, 16, 13 ] , [ 16, 5, 15, 16 ] , [ 17, 0, 12, 13 ]
  20B1 24 1 24 4 0 [ 1, 10, 5, 11 ] , [ 11, 0, 0, 11 ] , [ 16, 5, 15, 11 ] , [ 17, 8, 8, 5 ] , [ 19, 0, 0, 19 ] , [ 19, 6, 3, 1 ]
  20C1 24 2 6 4 0 [ 7, 2, 5, 13 ] , [ 11, 0, 10, 11 ] , [ 11, 10, 0, 11 ] , [ 16, 15, 5, 11 ] , [ 17, 8, 8, 5 ] , [ 19, 0, 0, 19 ]
  20D1 Γ0(20) 36 1 18 0 0 [ 1, 0, 10, 1 ] , [ 5, 12, 12, 17 ] , [ 5, 12, 17, 17 ] , [ 9, 0, 0, 9 ] , [ 9, 8, 16, 1 ] , [ 11, 0, 10, 11 ]
  20E1 36 1 18 4 0 [ 1, 0, 10, 1 ] , [ 5, 12, 12, 17 ] , [ 9, 0, 0, 9 ] , [ 9, 8, 16, 1 ] , [ 11, 0, 10, 11 ] , [ 15, 2, 17, 17 ]
  20F1 40 2 10 4 4 [ 1, 15, 15, 6 ] , [ 5, 14, 11, 15 ] , [ 9, 8, 8, 5 ] , [ 11, 0, 10, 11 ] , [ 11, 10, 0, 11 ] , [ 19, 0, 0, 19 ]
  20G1 48 1 24 8 0 [ 11, 0, 0, 11 ] , [ 13, 16, 16, 9 ] , [ 16, 5, 15, 11 ] , [ 19, 0, 0, 19 ] , [ 19, 6, 3, 1 ]
  20H1 72 1 18 0 0 [ 1, 0, 5, 1 ] , [ 1, 0, 10, 1 ] , [ 13, 12, 12, 5 ] , [ 17, 8, 8, 5 ] , [ 19, 4, 14, 3 ]
  20I1 72 1 18 8 0 [ 1, 0, 10, 1 ] , [ 13, 12, 12, 5 ] , [ 15, 6, 9, 5 ] , [ 17, 8, 8, 5 ] , [ 19, 4, 14, 3 ]
  20J1 72 2 18 4 0 [ 1, 4, 17, 9 ] , [ 11, 0, 10, 11 ] , [ 11, 10, 10, 11 ] , [ 13, 16, 16, 9 ] , [ 15, 12, 2, 7 ] , [ 19, 0, 0, 19 ]
^ Level 21 Name Index  con   len   c2   c3  > SL(2,Z/21Z) Matrix Generators
  21A1 24 2 8 0 3 [ 1, 0, 18, 1 ] , [ 1, 14, 14, 8 ] , [ 4, 0, 14, 16 ] , [ 8, 0, 0, 8 ] , [ 8, 14, 14, 1 ] , [ 13, 0, 0, 13 ] , [ 20, 0, 6, 20 ]
  21B1 Γ0(21) 32 1 32 0 2 [ 1, 0, 7, 1 ] , [ 1, 0, 14, 1 ] , [ 1, 0, 18, 1 ] , [ 8, 0, 0, 8 ] , [ 13, 0, 0, 13 ] , [ 16, 0, 0, 4 ] , [ 20, 0, 20, 20 ]
  21C1 42 2 14 6 3 [ 1, 14, 14, 8 ] , [ 4, 0, 2, 16 ] , [ 7, 10, 16, 14 ] , [ 7, 18, 12, 7 ] , [ 8, 0, 0, 8 ] , [ 11, 0, 16, 2 ] , [ 13, 0, 0, 13 ] , [ 15, 7, 14, 15 ] , [ 16, 9, 15, 19 ]
  21D1 42 2 21 10 0 [ 2, 5, 20, 19 ] , [ 4, 6, 3, 10 ] , [ 4, 18, 0, 16 ] , [ 7, 18, 12, 7 ] , [ 8, 0, 0, 8 ] , [ 13, 0, 0, 13 ] , [ 15, 14, 7, 15 ]
  21E1 63 1 21 15 0 [ 4, 6, 3, 10 ] , [ 7, 18, 12, 7 ] , [ 8, 0, 0, 8 ] , [ 8, 7, 7, 1 ] , [ 8, 14, 14, 1 ] , [ 13, 0, 0, 13 ] , [ 16, 12, 6, 19 ]
  21F1 64 1 32 0 4 [ 1, 0, 7, 1 ] , [ 1, 0, 9, 1 ] , [ 4, 0, 15, 16 ] , [ 20, 0, 7, 20 ] , [ 20, 0, 14, 20 ]
^ Level 22 Name Index  con   len   c2   c3  > SL(2,Z/22Z) Matrix Generators
  22A1 22 2 11 0 4 [ 0, 13, 5, 21 ] , [ 11, 8, 4, 11 ] , [ 12, 11, 11, 1 ] , [ 21, 0, 0, 21 ]
^ Level 24 Name Index  con   len   c2   c3  > SL(2,Z/24Z) Matrix Generators
  24A1 24 2 4 6 0 [ 1, 16, 16, 17 ] , [ 3, 8, 4, 3 ] , [ 4, 15, 9, 4 ] , [ 7, 0, 0, 7 ] , [ 13, 0, 12, 13 ] , [ 13, 9, 9, 10 ] , [ 13, 12, 0, 13 ] , [ 13, 16, 4, 5 ] , [ 17, 0, 0, 17 ] , [ 19, 0, 12, 19 ]
  24B1 24 2 12 6 0 [ 1, 4, 16, 17 ] , [ 4, 13, 19, 20 ] , [ 4, 15, 9, 4 ] , [ 7, 0, 0, 7 ] , [ 12, 11, 13, 12 ] , [ 13, 0, 12, 13 ] , [ 13, 9, 9, 10 ] , [ 13, 12, 0, 13 ] , [ 17, 0, 0, 17 ] , [ 19, 0, 12, 19 ]
  24C1 36 1 6 6 0 [ 1, 0, 6, 1 ] , [ 1, 0, 12, 1 ] , [ 1, 0, 18, 1 ] , [ 1, 8, 20, 17 ] , [ 1, 16, 4, 17 ] , [ 7, 0, 0, 7 ] , [ 13, 0, 12, 13 ] , [ 17, 0, 0, 17 ] , [ 19, 0, 12, 19 ] , [ 19, 18, 3, 13 ]
  24D1 36 1 9 8 0 [ 1, 0, 12, 1 ] , [ 1, 16, 10, 17 ] , [ 7, 0, 0, 7 ] , [ 9, 8, 16, 9 ] , [ 13, 0, 12, 13 ] , [ 13, 12, 6, 13 ] , [ 13, 12, 18, 13 ] , [ 17, 0, 0, 17 ] , [ 19, 0, 12, 19 ] , [ 19, 10, 7, 5 ]
  24E1 36 1 18 6 0 [ 1, 0, 6, 1 ] , [ 1, 0, 12, 1 ] , [ 7, 0, 0, 7 ] , [ 9, 8, 16, 9 ] , [ 13, 0, 12, 13 ] , [ 13, 4, 4, 5 ] , [ 13, 4, 22, 5 ] , [ 17, 0, 0, 17 ] , [ 19, 0, 12, 19 ] , [ 19, 18, 3, 13 ]
  24F1 48 1 16 12 0 [ 1, 1, 13, 14 ] , [ 1, 9, 21, 22 ] , [ 4, 9, 15, 4 ] , [ 7, 0, 0, 7 ] , [ 17, 0, 0, 17 ] , [ 17, 8, 8, 1 ] , [ 17, 16, 16, 1 ] , [ 19, 0, 0, 19 ]
  24G1 Γ0(24) 48 1 24 0 0 [ 1, 0, 12, 1 ] , [ 1, 0, 18, 1 ] , [ 1, 8, 0, 1 ] , [ 5, 0, 6, 5 ] , [ 7, 0, 12, 7 ] , [ 13, 0, 0, 13 ] , [ 13, 0, 12, 13 ] , [ 17, 0, 9, 17 ] , [ 23, 0, 0, 23 ]
  24H1 72 1 9 16 0 [ 1, 0, 12, 1 ] , [ 1, 12, 18, 1 ] , [ 9, 8, 16, 9 ] , [ 13, 0, 12, 13 ] , [ 17, 0, 0, 17 ] , [ 19, 0, 12, 19 ] , [ 23, 2, 23, 1 ]
  24I1 72 1 18 4 0 [ 1, 0, 12, 1 ] , [ 1, 0, 18, 1 ] , [ 1, 10, 4, 17 ] , [ 5, 14, 23, 7 ] , [ 11, 0, 12, 11 ] , [ 13, 0, 12, 13 ] , [ 17, 12, 18, 17 ] , [ 19, 12, 18, 19 ] , [ 23, 0, 0, 23 ] , [ 23, 0, 21, 23 ]
  24J1 96 1 24 0 0 [ 1, 0, 6, 1 ] , [ 1, 0, 12, 1 ] , [ 1, 8, 0, 1 ] , [ 11, 0, 6, 11 ] , [ 13, 0, 3, 13 ] , [ 13, 0, 18, 13 ] , [ 23, 0, 3, 23 ]
^ Level 26 Name Index  con   len   c2   c3  > SL(2,Z/26Z) Matrix Generators
  26A1 28 1 14 0 4 [ 5, 20, 16, 7 ] , [ 11, 14, 16, 11 ] , [ 13, 16, 4, 15 ] , [ 14, 13, 13, 1 ] , [ 17, 0, 24, 23 ]
  26B1 56 1 14 0 8 [ 3, 18, 0, 9 ] , [ 5, 2, 22, 9 ] , [ 14, 13, 13, 1 ] , [ 21, 18, 24, 7 ]
^ Level 27 Name Index  con   len   c2   c3  > SL(2,Z/27Z) Matrix Generators
  27A1 Γ0(27) 36 1 12 0 0 [ 1, 0, 18, 1 ] , [ 10, 0, 0, 19 ] , [ 10, 0, 24, 19 ] , [ 16, 18, 25, 13 ] , [ 25, 0, 14, 13 ] , [ 26, 0, 0, 26 ]
  27B1 36 1 12 0 6 [ 1, 0, 18, 1 ] , [ 1, 18, 6, 1 ] , [ 10, 0, 9, 19 ] , [ 10, 15, 25, 16 ] , [ 19, 0, 0, 10 ] , [ 19, 3, 17, 7 ] , [ 26, 0, 0, 26 ]
  27C1 108 1 12 0 0 [ 1, 0, 18, 1 ] , [ 10, 0, 0, 19 ] , [ 19, 0, 24, 10 ] , [ 25, 9, 20, 4 ] , [ 26, 0, 0, 26 ]
^ Level 28 Name Index  con   len   c2   c3  > SL(2,Z/28Z) Matrix Generators
  28A1 28 2 28 6 1 [ 1, 16, 4, 9 ] , [ 5, 8, 16, 9 ] , [ 13, 0, 0, 13 ] , [ 15, 0, 0, 15 ] , [ 15, 7, 14, 1 ] , [ 21, 12, 4, 21 ] , [ 22, 21, 21, 1 ] , [ 25, 12, 0, 9 ]
^ Level 30 Name Index  con   len   c2   c3  > SL(2,Z/30Z) Matrix Generators
  30A1 30 1 10 0 6 [ 1, 10, 10, 11 ] , [ 1, 20, 20, 11 ] , [ 1, 24, 18, 13 ] , [ 7, 6, 0, 13 ] , [ 11, 0, 0, 11 ] , [ 16, 15, 25, 1 ] , [ 19, 0, 0, 19 ] , [ 19, 12, 24, 1 ] , [ 21, 10, 20, 21 ]
  30B1 30 2 5 0 6 [ 1, 15, 15, 16 ] , [ 1, 18, 6, 19 ] , [ 7, 0, 12, 13 ] , [ 11, 0, 0, 11 ] , [ 11, 10, 10, 1 ] , [ 19, 0, 0, 19 ] , [ 19, 24, 16, 25 ] , [ 21, 20, 10, 21 ]
  30C1 36 1 18 8 0 [ 1, 25, 10, 11 ] , [ 7, 18, 18, 25 ] , [ 11, 0, 0, 11 ] , [ 16, 15, 15, 1 ] , [ 21, 25, 20, 21 ] , [ 27, 25, 2, 3 ] , [ 29, 0, 0, 29 ]
  30D1 72 1 18 16 0 [ 1, 15, 15, 16 ] , [ 11, 0, 0, 11 ] , [ 13, 6, 6, 19 ] , [ 13, 10, 13, 17 ] , [ 19, 0, 0, 19 ] , [ 21, 10, 20, 21 ]
^ Level 32 Name Index  con   len   c2   c3  > SL(2,Z/32Z) Matrix Generators
  32A1 Γ0(32) 48 1 12 0 0 [ 1, 16, 16, 1 ] , [ 1, 28, 12, 17 ] , [ 5, 20, 12, 29 ] , [ 9, 8, 24, 25 ] , [ 9, 24, 8, 25 ] , [ 11, 26, 6, 23 ] , [ 13, 4, 12, 21 ] , [ 15, 18, 6, 3 ] , [ 17, 10, 6, 13 ] , [ 17, 16, 16, 17 ] , [ 19, 26, 22, 15 ] , [ 26, 29, 27, 8 ]
  32B1 48 1 12 12 0 [ 0, 5, 19, 0 ] , [ 1, 8, 8, 1 ] , [ 1, 16, 16, 1 ] , [ 9, 6, 6, 29 ] , [ 9, 8, 8, 25 ] , [ 13, 6, 22, 25 ] , [ 17, 16, 16, 17 ] , [ 21, 4, 4, 13 ] , [ 25, 28, 28, 25 ] , [ 31, 0, 0, 31 ]
  32C1 48 1 24 2 0 [ 0, 7, 9, 0 ] , [ 1, 16, 16, 1 ] , [ 7, 4, 12, 7 ] , [ 9, 16, 16, 25 ] , [ 9, 24, 8, 25 ] , [ 13, 8, 8, 5 ] , [ 16, 15, 17, 16 ] , [ 17, 0, 0, 17 ] , [ 21, 28, 4, 13 ] , [ 26, 25, 27, 26 ] , [ 29, 28, 4, 5 ]
  32D1 48 1 24 2 0 [ 0, 7, 9, 0 ] , [ 1, 16, 16, 1 ] , [ 7, 4, 12, 7 ] , [ 9, 16, 16, 25 ] , [ 9, 24, 8, 25 ] , [ 11, 22, 26, 23 ] , [ 13, 8, 8, 5 ] , [ 17, 0, 0, 17 ] , [ 21, 28, 4, 13 ] , [ 26, 25, 27, 10 ] , [ 29, 28, 4, 5 ]
  32E1 96 1 12 0 0 [ 5, 12, 4, 29 ] , [ 5, 30, 18, 25 ] , [ 9, 8, 24, 25 ] , [ 11, 26, 6, 23 ] , [ 13, 14, 18, 17 ] , [ 17, 0, 0, 17 ] , [ 17, 2, 30, 13 ] , [ 17, 16, 16, 17 ] , [ 18, 25, 23, 16 ] , [ 21, 20, 12, 13 ] , [ 21, 28, 20, 13 ]
^ Level 33 Name Index  con   len   c2   c3  > SL(2,Z/33Z) Matrix Generators
  33A1 33 2 11 9 0 [ 1, 11, 11, 23 ] , [ 10, 17, 29, 23 ] , [ 12, 26, 13, 9 ] , [ 23, 0, 0, 23 ] , [ 23, 11, 11, 1 ] , [ 32, 0, 0, 32 ]
^ Level 36 Name Index  con   len   c2   c3  > SL(2,Z/36Z) Matrix Generators
  36A1 36 1 36 10 0 [ 1, 4, 28, 5 ] , [ 1, 9, 9, 10 ] , [ 17, 0, 0, 17 ] , [ 19, 0, 0, 19 ] , [ 25, 0, 12, 13 ] , [ 25, 24, 24, 13 ] , [ 28, 27, 9, 28 ] , [ 29, 28, 4, 25 ]
  36B1 48 1 8 0 6 [ 1, 0, 20, 1 ] , [ 1, 0, 24, 1 ] , [ 1, 18, 18, 1 ] , [ 13, 0, 0, 25 ] , [ 19, 0, 18, 19 ] , [ 22, 3, 15, 25 ] , [ 35, 0, 0, 35 ]
  36C1 Γ0(36) 72 1 12 0 0 [ 1, 0, 12, 1 ] , [ 1, 0, 18, 1 ] , [ 1, 0, 27, 1 ] , [ 13, 0, 0, 25 ] , [ 19, 0, 18, 19 ] , [ 25, 0, 20, 13 ] , [ 35, 0, 0, 35 ]
^ Level 39 Name Index  con   len   c2   c3  > SL(2,Z/39Z) Matrix Generators
  39A1 42 2 14 6 3 [ 1, 26, 26, 14 ] , [ 4, 0, 37, 10 ] , [ 7, 6, 10, 31 ] , [ 13, 3, 30, 28 ] , [ 14, 0, 0, 14 ] , [ 14, 26, 26, 1 ] , [ 27, 26, 13, 27 ] , [ 37, 27, 16, 37 ]
^ Level 40 Name Index  con   len   c2   c3  > SL(2,Z/40Z) Matrix Generators
  40A1 72 2 18 4 0 [ 1, 20, 20, 1 ] , [ 9, 0, 20, 9 ] , [ 9, 8, 26, 1 ] , [ 11, 10, 30, 31 ] , [ 14, 15, 25, 24 ] , [ 17, 8, 8, 25 ] , [ 21, 20, 20, 21 ] , [ 21, 30, 30, 1 ]
^ Level 42 Name Index  con   len   c2   c3  > SL(2,Z/42Z) Matrix Generators
  42A1 42 2 7 12 0 [ 7, 12, 18, 7 ] , [ 7, 24, 30, 13 ] , [ 13, 0, 0, 13 ] , [ 15, 14, 28, 15 ] , [ 22, 21, 21, 1 ] , [ 29, 0, 0, 29 ] , [ 29, 14, 14, 1 ] , [ 37, 6, 12, 19 ] , [ 41, 26, 17, 19 ]
  42B1 42 2 21 12 0 [ 7, 12, 18, 7 ] , [ 7, 24, 30, 13 ] , [ 13, 0, 0, 13 ] , [ 13, 12, 24, 19 ] , [ 15, 14, 7, 15 ] , [ 22, 21, 21, 1 ] , [ 29, 0, 0, 29 ] , [ 29, 14, 35, 1 ] , [ 37, 6, 12, 19 ]
^ Level 49 Name Index  con   len   c2   c3  > SL(2,Z/49Z) Matrix Generators
  49A1 Γ0(49) 56 1 56 0 2 [ 6, 44, 5, 45 ] , [ 22, 0, 42, 29 ] , [ 25, 21, 2, 37 ] , [ 29, 7, 14, 22 ] , [ 48, 0, 0, 48 ]
^ Level 52 Name Index  con   len   c2   c3  > SL(2,Z/52Z) Matrix Generators
  52A1 56 2 14 4 8 [ 5, 20, 16, 33 ] , [ 13, 16, 4, 41 ] , [ 14, 39, 39, 1 ] , [ 27, 0, 26, 27 ] , [ 27, 26, 0, 27 ] , [ 33, 16, 31, 45 ] , [ 41, 6, 32, 25 ]

Chris Cummins and Sebastian Pauli, computed with MAGMA