Dan Yasaki
Cohomology of Congruence Subgroups of \(\mathrm{SL}_3(\mathbb{Z})\), Steinberg Modules, and Real Quadratic Fields
Hecke Operator Matrix Data
The data files (plain text files) have the data format as follows:
Line 1 is N:dim, where N = level; dim = dimension of the cohomology \(H^3(\Gamma_0(N),\mathbb{Q})\)
Each following line is p:k:L, where L = list of entries in the matrix of the Hecke operator \(T(p,k)\).
6-ho 97-ho 121-ho 83-ho 89-ho 73-ho 79-ho 67-ho 71-ho 59-ho 61-ho 50-ho 53-ho 48-ho 49-ho 46-ho 47-ho 44-ho 45-ho 42-ho 43-ho 40-ho 41-ho 38-ho 39-ho 36-ho 37-ho 35-ho 33-ho 34-ho 31-ho 32-ho 29-ho 30-ho 27-ho 28-ho 25-ho 26-ho 23-ho 24-ho 21-ho 22-ho 19-ho 20-ho 17-ho 18-ho 15-ho 16-ho 12-ho 14-ho 10-ho 11-ho 8-ho 9-ho 4-ho 169-ho
Data
The data file (plain text file) has the data format as follows:
Each line is N:sqfree:dim:dimP:B, where N = level, sqfree = d squarefree defining real quadratic field \(\mathbb{Q}(\sqrt{d})\), dim = dimension of the cohomology \(H^3(\Gamma_0(N),\mathbb{Q})\), dimP = dimension of image of \(\psi\) found, B = list of entries of the echelon form of a matrix whose rows form a basis for the image.
Code
The code files (plain text files) compute the image of \(\psi\). The gl3.txt file is a data file that gets loaded in by all_gl3.mag. (Note: The server would not allow .mag extension, so there is an additional .txt on the file name.)
