TITLE: Symmetric powers of Ramanujan tau-function
QUESTION [6 upvotes]: Let $\Delta(z)$ be the modular form associated with Ramanujan $\tau$-function.
For any $k=2,3,...$, $Sym^k\Delta$ is conjectured to be an automorphic form on $\mathrm{GL}(k+1)$ and $L(s, Sym^k\Delta)$ is conjectured to be holomorphic and satisfies a functional equation. 
Question 1: For which $k$, has $Sym^k\Delta$ been proved to be automorphic form on $\mathrm{GL}(k+1)$? 
Question 2: For which $k$, has $L(s,Sym^k\Delta)$ been proved to be homorphic and satisfies a functional equation?
I know certainly that both questions is YES for $k=2,3,4$ (Gelbart-Jacquet, Kim-Shahidi, Shahidi). But I heard there is progress beyond that because $\Delta$ is a modular form rather than arbitrary automorphic representation on $\mathrm{GL}(2)$.

REPLY [10 votes]: According to this exciting new preprint of Newton and Thorne (https://arxiv.org/abs/1912.11261), the answer to both Questions 1 and 2 is "all $k\geq 1$".