Euler characteristic and cohomology of $\mathrm{Sp}_4(\mathbb{Z})$ with nontrivial coefficients

Abstract

In this article, the cohomology of the arithmetic group Sp 4 (Z) with coefficients in any finite dimensional highest weight representation M λ have been studied. Euler characteristic with coefficients in M λ have been carried out in detail. Combining the results obtained on Euler characteristic and the work of Harder on Eisenstein cohomology [9], the description of the cuspidal cohomology has been achieved. At the end, we employ our study to compute the dimensions for the cohomology spaces H • (Sp 4 (Z), M λ ).