The non-CM Fourier coefficient conjecture for odd discriminant level

Let $k$ be an integer with $k\geq 3$, and let $D=p_1\cdots p_\ell$ be an odd discriminant. Let $S_k^{\mathrm{Ell}}(\Gamma_1(D),\omega_{E/\mathbb{Q}})$ denote the space of elliptic cusp forms of weight $k$, level $\Gamma_1(D)$, and nebentypus $\omega_{E/\mathbb{Q}}$. A normalized newform in this space is non-CM if it does not have complex multiplication. The non-CM Fourier coefficient conjecture. If this space contains a non-CM normalized newform, then at least one such newform $f$ satisfies

$$a_f(p_i)\neq \pm p_i^{(k-1)/2}\quad\text{for every }i.$$

Here $a_f(p_i)$ is the $p_i$-th Fourier coefficient of $f$. This conjecture asserts that, among the available non-CM newforms, one can find a form avoiding the CM-type extremal values at every prime dividing the odd discriminant. The source provides no resolution, so the conjecture is recorded as open.