Dimensions of cusp forms for Γ₀(p) in degree two and small weights

摘要

We investigate degree two Siegel cusp forms of small weight for Γ₀(p). Using the Restriction Technique we compute some dimensions and verify the conjectures ofHashimoto in some examples of weights three and four. For weight two we determine the dimension for primesp ≤ 41 and find only lifts. We explain in general how to compute spaces of Siegel cusp forms for subgroups of finite index in Γ _n .