Cohomology of Congruence Subgroups of SL4(Z). III
Abstract
In two previous papers [AGM1, AGM2] we computed cohomology groups H5(Γ0 (N); ) for a range of levels N, where Γ0 (N) is the congruence subgroup of SL4 () 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 H5(Γ0 (N); ) for N prime coming from Eisenstein series and Siegel modular forms.
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