Toric Periods and $p$-adic Families of Modular Forms of Half-Integral Weight Max Wainewright Many are not achieving their

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Toric Periods and $p$-adic Families of Modular Forms of Half-Integral Weight Max Wainewright Many are not achieving theirThe primary goal of this work is to construct $p$ adic families of modular forms of half integral weight, by using Waldspurger's automorphic framework to make the results as comprehensive and precise as possible. A secondary goal is to clarify the role of test vectors as defined by Gross Prasad in the elucidation of general formulae for the Fourier coefficients of modular forms of half integral weight in terms of toric periods of the corresponding