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Questions about half-integral weight modular forms, and more generally automorphic representations associated to metaplectic groups.
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The space of lattices and modular forms of weight 1/2
Suppose my favorite way of thinking about modular forms is as functions on the space of (real, 2D) lattices. One can identify this space with $SL_2(\mathbb{Z}) \backslash GL_2(\mathbb{R})$, i.e. base …