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Eigenvalue of Fricke involution on newforms of level 4 and of trivial character

In this note, we consider the newforms of integral weight, level 4 and of trivial character, and prove that all of them are actually level 1 forms of some non-Dirichlet character. As a byproduct, we can prove that all of them are eigenfunctions of the Fricke involution with eigenvalue -1.

preprint2013arXivOpen access
Yichao Zhang
math.NT
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Yichao Zhang

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