Cohomology of Congruence Subgroups of SL_4(Z). III
arXiv:0903.3201
Abstract
In two previous papers [AGM1, AGM2] we computed cohomology groups H^5(Γ_0 (N); \C) for a range of levels N, where Γ_0 (N) is the congruence subgroup of SL_4 (\Z) consisting of all matrices with bottom row congruent to (0,0,0,*) mod N. In this note we update this earlier work by carrying it out for prime levels up to N = 211. This requires new methods in sparse matrix reduction, which are the main focus of the paper. Our computations involve matrices with up to 20 million non-zero entries. We also make two conjectures concerning the contributions to H^5(Γ_0 (N); \C) for N prime coming from Eisenstein series and Siegel modular forms.
incorporates referees' comments
Cited by in corpus (7)
- Stability in the high-dimensional cohomology of congruence subgroups
- On the integral homology of PSL4(Z) and other arithmetic groups
- Computing Hecke Operators for Arithmetic Subgroups of General Linear Groups
- On the cohomology of congruence subgroups of SL_4 (\Z)
- Torsion in the cohomology of congruence subgroups of SL(4,Z) and Galois representations
- Mod 2 homology for GL(4) and Galois representations
- Resolutions of the Steinberg module for GL(n)