[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 > 6A1 6B1 6C1 6D1 6E1 Name Index con len c2 c3 SL(2,Z/6Z) Matrix Generators 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 ] 12 1 3 0 0 [ 1, 5, 5, 2 ] , [ 4, 3, 3, 1 ] , [ 5, 0, 0, 5 ] , [ 5, 4, 4, 1 ] 18 1 1 0 0 [ 1, 4, 4, 5 ] , [ 3, 4, 2, 3 ] , [ 5, 0, 0, 5 ] 24 1 1 0 0 [ 4, 3, 3, 1 ] , [ 5, 0, 0, 5 ] 36 1 3 0 0 [ 5, 0, 0, 5 ] , [ 5, 4, 4, 1 ] Γ(6) 72 1 1 0 0 [ 5, 0, 0, 5 ] Name Index con len c2 c3 SL(2,Z/7Z) Matrix Generators 42 1 21 2 0 [ 2, 5, 6, 5 ] , [ 6, 0, 0, 6 ] , [ 6, 3, 5, 5 ] 56 1 28 0 2 [ 4, 0, 2, 2 ] , [ 6, 0, 0, 6 ] 84 1 21 4 0 [ 0, 3, 2, 0 ] , [ 6, 0, 0, 6 ] Name Index con len c2 c3 SL(2,Z/8Z) Matrix Generators 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 ] 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 ] 24 1 6 0 0 [ 1, 4, 4, 1 ] , [ 4, 1, 7, 0 ] , [ 5, 0, 0, 5 ] , [ 7, 4, 4, 7 ] 24 1 12 2 0 [ 1, 4, 4, 1 ] , [ 4, 1, 7, 0 ] , [ 5, 0, 4, 5 ] , [ 7, 4, 4, 7 ] 32 1 16 0 2 [ 2, 3, 3, 5 ] , [ 3, 0, 0, 3 ] , [ 7, 0, 0, 7 ] 48 1 3 0 0 [ 3, 0, 0, 3 ] , [ 7, 0, 0, 7 ] , [ 7, 4, 4, 7 ] 48 1 6 0 0 [ 1, 4, 0, 1 ] , [ 3, 2, 4, 3 ] , [ 7, 4, 0, 7 ] 48 1 12 4 0 [ 0, 3, 5, 0 ] , [ 1, 4, 4, 1 ] , [ 7, 4, 4, 7 ] 48 1 12 4 0 [ 0, 1, 7, 0 ] , [ 0, 5, 3, 0 ] , [ 7, 0, 0, 7 ] 64 1 16 0 4 [ 2, 3, 3, 5 ] , [ 7, 0, 0, 7 ] 96 1 3 0 0 [ 5, 4, 4, 5 ] , [ 7, 0, 0, 7 ] Name Index con len c2 c3 SL(2,Z/9Z) Matrix Generators 12 1 4 0 0 [ 4, 0, 6, 7 ] , [ 4, 6, 5, 1 ] , [ 7, 0, 6, 4 ] , [ 8, 0, 0, 8 ] 18 2 9 2 0 [ 1, 7, 1, 8 ] , [ 4, 6, 6, 7 ] , [ 5, 3, 3, 2 ] , [ 7, 0, 0, 4 ] 36 1 4 0 0 [ 1, 0, 6, 1 ] , [ 4, 0, 3, 7 ] , [ 8, 0, 0, 8 ] 36 1 12 0 0 [ 1, 0, 6, 1 ] , [ 7, 6, 5, 7 ] , [ 8, 0, 0, 8 ] 54 1 18 6 0 [ 0, 1, 8, 0 ] , [ 7, 0, 0, 4 ] , [ 8, 0, 0, 8 ] 54 2 9 6 0 [ 0, 1, 8, 0 ] , [ 5, 3, 3, 2 ] , [ 7, 3, 3, 4 ] 81 1 27 9 0 [ 1, 5, 5, 8 ] , [ 4, 1, 1, 5 ] , [ 5, 8, 8, 4 ] , [ 8, 0, 0, 8 ] 108 1 4 0 0 [ 1, 0, 3, 1 ] , [ 8, 0, 0, 8 ] Name Index con len c2 c3 SL(2,Z/10Z) Matrix Generators 12 1 6 0 0 [ 6, 5, 5, 1 ] , [ 7, 8, 8, 5 ] , [ 9, 0, 0, 9 ] , [ 9, 6, 8, 1 ] 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 ] 20 1 10 0 2 [ 1, 5, 5, 6 ] , [ 7, 4, 0, 3 ] , [ 9, 0, 0, 9 ] , [ 9, 8, 8, 5 ] 24 1 6 0 0 [ 3, 6, 6, 9 ] , [ 6, 5, 5, 1 ] , [ 9, 0, 0, 9 ] 30 1 15 4 0 [ 3, 4, 5, 7 ] , [ 6, 5, 5, 1 ] , [ 7, 0, 2, 3 ] , [ 9, 0, 0, 9 ] 30 1 30 2 0 [ 1, 0, 5, 1 ] , [ 7, 4, 5, 3 ] , [ 9, 0, 0, 9 ] , [ 9, 8, 8, 5 ] 36 1 6 0 0 [ 5, 2, 2, 7 ] , [ 9, 0, 0, 9 ] , [ 9, 8, 6, 1 ] 40 1 10 0 4 [ 6, 5, 5, 1 ] , [ 9, 0, 0, 9 ] , [ 9, 8, 8, 5 ] 45 1 15 3 0 [ 1, 0, 5, 1 ] , [ 3, 4, 5, 7 ] , [ 7, 0, 2, 3 ] , [ 9, 0, 0, 9 ] 60 1 60 4 3 [ 5, 4, 1, 5 ] , [ 9, 0, 0, 9 ] , [ 9, 3, 3, 0 ] 72 1 6 0 0 [ 3, 6, 6, 9 ] , [ 5, 2, 2, 7 ] , [ 9, 0, 0, 9 ] Name Index con len c2 c3 SL(2,Z/11Z) Matrix Generators Γ0(11) 12 1 12 0 0 [ 7, 0, 7, 8 ] , [ 8, 1, 6, 5 ] , [ 10, 0, 0, 10 ] 55 1 55 3 4 [ 3, 1, 1, 8 ] , [ 3, 5, 3, 9 ] , [ 6, 7, 1, 5 ] , [ 10, 0, 0, 10 ] 55 1 55 7 1 [ 0, 10, 1, 0 ] , [ 1, 8, 8, 10 ] , [ 3, 9, 9, 9 ] , [ 10, 0, 0, 10 ] Γ1(11) 60 1 12 0 0 [ 4, 2, 1, 9 ] , [ 10, 0, 0, 10 ] Name Index con len c2 c3 SL(2,Z/12Z) Matrix Generators 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 ] 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 ] 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 ] 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 ] 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 ] 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 ] 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 ] 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 ] 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 ] 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 ] 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 ] 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 ] 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 ] 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 ] 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 ] 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 ] 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 ] 64 1 16 0 4 [ 1, 0, 4, 1 ] , [ 1, 0, 8, 1 ] , [ 10, 3, 3, 1 ] , [ 11, 0, 4, 11 ] 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 ] 72 1 9 8 0 [ 4, 11, 5, 8 ] , [ 5, 0, 0, 5 ] , [ 7, 0, 0, 7 ] , [ 7, 6, 6, 7 ] 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 ] 96 1 12 0 0 [ 1, 0, 6, 1 ] , [ 5, 4, 8, 9 ] , [ 7, 8, 10, 3 ] , [ 9, 8, 4, 5 ] Name Index con len c2 c3 SL(2,Z/14Z) Matrix Generators 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 ] 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 ] Γ0(14) 24 1 24 0 0 [ 1, 0, 7, 1 ] , [ 11, 8, 12, 5 ] , [ 13, 10, 2, 7 ] , [ 13, 12, 12, 9 ] 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 ] 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 ] 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 ] 56 1 28 8 2 [ 1, 7, 7, 8 ] , [ 1, 12, 1, 13 ] , [ 9, 2, 0, 11 ] , [ 13, 0, 0, 13 ] Γ1(14) 72 1 24 0 0 [ 3, 3, 8, 13 ] , [ 5, 6, 2, 11 ] , [ 11, 8, 12, 5 ] , [ 11, 11, 6, 1 ] Name Index con len c2 c3 SL(2,Z/15Z) Matrix Generators 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 ] 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 ] 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 ] 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 ] 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 ] 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 ] 48 1 24 0 0 [ 1, 0, 5, 1 ] , [ 4, 0, 10, 4 ] , [ 7, 3, 3, 10 ] , [ 11, 0, 5, 11 ] 72 1 18 8 0 [ 4, 0, 0, 4 ] , [ 5, 12, 12, 2 ] , [ 10, 4, 1, 5 ] , [ 13, 6, 6, 4 ] Γ1(15) 96 1 24 0 0 [ 1, 0, 5, 1 ] , [ 1, 0, 10, 1 ] , [ 8, 12, 7, 5 ] , [ 13, 6, 6, 4 ] Name Index con len c2 c3 SL(2,Z/16Z) Matrix Generators 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 ] 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 ] 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 ] 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 ] 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 ] 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 ] 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 ] 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 ] 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 ] 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 ] 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 ] 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 ] 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 ] Name Index con len c2 c3 SL(2,Z/17Z) Matrix Generators 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 ] 36 1 18 4 0 [ 1, 0, 8, 1 ] , [ 4, 0, 14, 13 ] , [ 15, 0, 8, 8 ] , [ 16, 0, 0, 16 ] 72 1 18 8 0 [ 1, 0, 2, 1 ] , [ 13, 0, 15, 4 ] , [ 16, 0, 0, 16 ] Name Index con len c2 c3 SL(2,Z/18Z) Matrix Generators 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 ] 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 ] 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 ] 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 ] 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 ] 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 ] 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 ] 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 ] 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 ] 72 1 4 0 0 [ 1, 0, 12, 1 ] , [ 7, 0, 2, 13 ] , [ 13, 0, 0, 7 ] , [ 17, 0, 0, 17 ] 72 1 8 0 9 [ 1, 0, 6, 1 ] , [ 7, 0, 6, 13 ] , [ 16, 15, 7, 1 ] , [ 17, 0, 0, 17 ] Name Index con len c2 c3 SL(2,Z/19Z) Matrix Generators Γ0(19) 20 1 20 0 2 [ 0, 18, 1, 1 ] , [ 2, 7, 12, 14 ] , [ 3, 5, 3, 18 ] , [ 18, 0, 0, 18 ] 60 1 20 0 6 [ 11, 0, 6, 7 ] , [ 16, 9, 13, 5 ] , [ 18, 0, 0, 18 ] Name Index con len c2 c3 SL(2,Z/20Z) Matrix Generators 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 ] 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 ] 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 ] 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 ] 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 ] 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 ] 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 ] 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 ] 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 ] 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 ] Name Index con len c2 c3 SL(2,Z/21Z) Matrix Generators 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 ] 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 ] 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 ] 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 ] 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 ] 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 ] Name Index con len c2 c3 SL(2,Z/22Z) Matrix Generators 22 2 11 0 4 [ 0, 13, 5, 21 ] , [ 11, 8, 4, 11 ] , [ 12, 11, 11, 1 ] , [ 21, 0, 0, 21 ] Name Index con len c2 c3 SL(2,Z/24Z) Matrix Generators 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 ] 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 ] 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 ] 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 ] 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 ] 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 ] 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 ] 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 ] 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 ] 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 ] Name Index con len c2 c3 SL(2,Z/26Z) Matrix Generators 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 ] 56 1 14 0 8 [ 3, 18, 0, 9 ] , [ 5, 2, 22, 9 ] , [ 14, 13, 13, 1 ] , [ 21, 18, 24, 7 ] Name Index con len c2 c3 SL(2,Z/27Z) Matrix Generators 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 ] 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 ] 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 ] Name Index con len c2 c3 SL(2,Z/28Z) Matrix Generators 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 ] Name Index con len c2 c3 SL(2,Z/30Z) Matrix Generators 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 ] 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 ] 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 ] 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 ] Name Index con len c2 c3 SL(2,Z/32Z) Matrix Generators 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 ] 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 ] 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 ] 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 ] 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 ] Name Index con len c2 c3 SL(2,Z/33Z) Matrix Generators 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 ] Name Index con len c2 c3 SL(2,Z/36Z) Matrix Generators 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 ] 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 ] 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 ] Name Index con len c2 c3 SL(2,Z/39Z) Matrix Generators 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 ] Name Index con len c2 c3 SL(2,Z/40Z) Matrix Generators 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 ] Name Index con len c2 c3 SL(2,Z/42Z) Matrix Generators 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 ] 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 ] Name Index con len c2 c3 SL(2,Z/49Z) Matrix Generators 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 ] Name Index con len c2 c3 SL(2,Z/52Z) Matrix Generators 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