Symmetric power functoriality for holomorphic modular forms

James Newton, Jack A. Thorne

Published 2019-12-24Version 1

Let $f$ be a cuspidal Hecke eigenform of level 1. We prove the automorphy of the symmetric power lifting $\mathrm{Sym}^n f$ for every $n \geq 1$. We establish the same result for a more general class of cuspidal Hecke eigenforms, including all those associated to semistable elliptic curves over $\mathbb{Q}$.