Cohomology of congruence subgroups of SL(4,Z)

Details Cohomology of congruence subgroups of SL(4,Z) Cohomology of congruence subgroups of SL(4,Z)

2000-03-30

arxiv.org/abs/math/0003219v1

Mathematics

Number Theory

29 pp

Scientific paper

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; \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.

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