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

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Basis for modular forms of half-integral weight

You might also try Eichler and Zagier's book on the theory of Jacobi forms. For example, they show how to compute half-integer weight mf's of weight k+1/2 and level N from Jacobi forms when k is odd. …
Kim Hopkins's user avatar