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

References in corpus (2)

• Adequate subgroups
• Sur la torsion dans la cohomologie des variétés de Shimura de Kottwitz-Harris-Taylor