Lehmer's conjecture for the Ramanujan tau coefficients

Let $q=e^{2\pi i z}$, and let

$$\Delta_k(z)=\sum_{n=1}^{\infty}\tau_k(n)q^n\in S_k^{\operatorname{new}}(\Gamma_0(1))$$

be a newform, where $k\in\{12,16,18,20,22,26\}$. Lehmer's conjecture. For every such $k$ and every positive integer $n$,

$$\tau_k(n)\neq0.$$

For $k=12$, this is Lehmer's question about the nonvanishing of the Ramanujan tau function, and the source states that it remains open, as do analogous questions for the other listed newforms.