J.-I. Igusa determined in the 1960s the dimension of the space of scalar-valued cusp forms on $\Sp(4,\Z)$. R. Tsushima gave in the 1980s formulas for the dimensions of the spaces of vector-valued cusp forms of degree $2$ and extended this to a subgroup of $\Gamma_2[2]$, see the references in [2] and [3]. Bergström extended this to $\Gamma_2[2]$ together with the action of $\Sp(4,\mathbb{Z}/2)$ (unpublished).

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