  Let A_2 be the moduli stack of principally polarized abelian surfaces and V a
smooth l-adic sheaf on A_2 associated to an irreducible rational finite
dimensional representation of Sp(4). We give an explicit expression for the
cohomology of V in any degree in terms of Tate type classes and Galois
representations attached to elliptic and Siegel cusp forms. This confirms a
conjecture of Faber and van der Geer. As an application we prove a dimension
formula for vector-valued Siegel cusp forms for Sp(4,Z) of weight three, which
had been conjectured by Ibukiyama.
