Symmetric power functoriality for holomorphic modular forms

Abstract

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 $n\ge 1$. We establish the same result for a more general class of cuspidal Hecke eigenforms, including all those associated to semistable elliptic curves over $\mathbb{Q}$.

Accepted version