Power-residue density conjecture for non-CM newforms

Let $f=\mathfrak{a}0\sum a_nq^n$ be a newform with rational Fourier coefficients, and let $m\geq 2$ be an integer. Define $\delta_m(f)$ as the relative density of the primes $p\equiv 1\pmod m$ for which $a_p$ is a nonzero $m$th power modulo $p$, among those for which $a_p\not\equiv 0\pmod p$. Power-residue density conjecture. If $f$ does not have complex multiplication, then

$$\delta_m(f)=\frac{1}{m}.$$

This conjecture predicts that non-CM modular forms have equidistributed power-residue behavior in their nonzero Fourier coefficients; the source presents it as being supported by computations, with no resolution stated.