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On the slopes of the $U_5$ operator acting on overconvergent modular forms

L. J. P. Kilford
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Abstract

We show that the slopes of the~$U_5$ operator acting on slopes of 5-adic overconvergent modular forms of weight~$k$ with primitive Dirichlet character~$χ$ of conductor~25 are given by either \[ \left\{{1/4}\cdot\lfloor\frac{8i}{5}\rfloor: i \in \N\right\}\text{or }\left\{{1/4}\cdot\lfloor\frac{8i+4}{5}\rfloor: i \in \N\right\}, \] depending on~$k$ and~$χ$.

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L. J. P. Kilford. 2006-06-15. On the slopes of the $U_5$ operator acting on overconvergent modular forms. https://arxiv.org/abs/math/0606363

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