Non-abelian base change for symmetric power liftings of holomorphic modular forms

Let $f$ be a non-CM Hecke eigenform of weight $k\ge 2$. We give a new proof of some cases of Langlands functoriality for the automorphic representation $\pi$ associated to $f$. More precisely, we prove the existence of the base change lifting, with respect to any totally real extension $F\mathrm{/}\mathbb{Q}$, of any symmetric power lifting of $\pi$.