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

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 $n = 1, 3, \dots, 25$.