Abstract: Let $N>1$ be an integer, and let $\Gamma = \Gamma _{0} (N) \subset SL (4,\Z)$ be the subgroup of matrices with bottom row congruent to $(0,0,0,*)\mod N$. We compute $H^{5} (\Gamma; R) $ for a range of $N$, and compute the action of the various 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.

BibTeX

@misc{math.NT/0003219,
    title = {{Cohomology of congruence subgroups of SL(4,Z)}},
    author = {Avner Ash and Paul E. Gunnells and and Mark McConnell},
    eprint = {arxiv:math.NT/0003219}}