Cohomology of Congruence Subgroups of SL4(image), Original Research Article

Let N>1 be an integer, and let Γ=Γ0(N)subset ofSL4(image) be the subgroup of matrices with bottom row congruent to (0, 0, 0, *) modN. We compute H5(Γ; image) for a range of N and compute the action of some Hecke operators on many of these groups. We relate the classes we find to classes coming from the boundary of the Borel–Serre compactification, to Eisenstein series, and to classical holomorphic modular forms of weights 2 and 4.