Let N > 1 be an integer, and let Γ = Γ0(N) ⊂ SL4 (ℤ) be the subgroup of matrices with bottom row congruent to (0, 0, 0, *) modN. We compute H5(Γ; ℂ) 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.
All Science Journal Classification (ASJC) codes
- Algebra and Number Theory
- Cohomology of arithmetic groups
- Hecke operators
- Modular symbols