A $p$-adic approach to the existence of level-raising congruences

Jack A. Thorne

A $p$-adic approach to the existence of level-raising congruences

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arxiv 2212.03591 v2 pith:M7UXW6B6 submitted 2022-12-07 math.NT

Jack A. Thorne This is my paper · ORCID

classification math.NT

keywords congruencesexistencehilbertlevel-raisingmodularpowersymmetricadic

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abstract

We construct level-raising congruences between $p$-ordinary automorphic representations, and apply this to the problem of symmetric power functoriality for Hilbert modular forms. In particular, we prove the existence of the $n^\text{th}$ symmetric power lift of a Hilbert modular eigenform of regular weight for each odd integer $n = 1, 3, \dots, 25$.

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