The Eisenstein motive for the cohomology of GSp2(Z)

In his paper [4], Gerard van der Geer discusses the Eisenstein cohomology with coefficients in a sheaf (Mu) over tilde, which is obtained from a representation for the group (Gamma) over tilde = GSp(g)(Z). Since we have an arithmetic interpretation of this sheaf, we can endow these cohomology groups with the structure of a mixed motive. A certain part of this cohomology is the compactly supported Eisenstein cohomology and van der Geer determines the structure of this compactly supported Eisenstein motive in the case g = 2 and a regular coefficient system ([4], Cor. 10.2). At the end of this note we compute this part of the cohomology for an arbitrary coefficient system, again in the case g = 2.