Abstract
If the modular group Γ=SL(2,ℤ) operates in the usual way on complex vector spaces generated by suitably chosen theta constants of level q (i.e. modular forms for the congruence subgroup Γ(q) of Γ), then this operation defines a representation of the group SL(2,ℤ/qℤ). Using this method, we construct all Weil representations of these groups for any prime-power q. It is shown how they depend on the underlying quadratic form of the theta constants and how theta relations can be used to find invariant subspaces.
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