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Using a description of the cohomology of local systems on the moduli space ofabelian surfaces with a full level two structure, together with a computationof Euler characteristics we find the isotypical decomposition, under thesymmetric group on 6 letters, of spaces of vector-valued Siegel modular formsof degree two and level two.

Dimension formulas for spaces of vector-valued Siegel modular forms of degree two and level two