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Questions about half-integral weight modular forms, and more generally automorphic representations associated to metaplectic groups.

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Half integral weight Hecke operators

I think you can find the answer here.
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4 votes
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No Exceptional Eigenvalues of Weight 1/2 Maass Forms on $\Gamma_0(4)$?

A weight $1/2$ Hecke-Maass form of eigenvalue $(1-s^2)/4$ on $\Gamma_0(4)$ has a Shimura lift to a weight $0$ even Hecke-Maass form of eigenvalue $1/4-s^2$ on $\Gamma_0(1)$, see e.g. the proof of Theo …
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