Symmetric power functoriality for holomorphic modular forms

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