Abstract
We consider the classical theta operator on modular forms modulo and level prime to , where is a prime greater than three. Our main result is that mod will map forms of weight to forms of weight and that this weight is optimal in certain cases when is at least two. Thus, the natural expectation that mod should map to weight is shown to be false. The primary motivation for this study is that application of the operator on eigenforms mod corresponds to twisting the attached Galois representations with the cyclotomic character. Our construction of the -operator mod gives an explicit weight bound on the twist of a modular mod Galois representation by the cyclotomic character.
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