Xue–Zhu conjecture on determining level-one eigenforms by Fourier coefficients

Let $m\geq 2$ be fixed, and let $f$ be a normalized Hecke eigenform of level one. Its $m$-th Fourier coefficient is the coefficient of $q^m$ in its normalized Fourier expansion. Xue–Zhu conjecture. The normalized Hecke eigenform $f$ is determined by its $m$-th Fourier coefficient. This extends the analogous result known for the second Fourier coefficient under Maeda's conjecture; the source attributes the question to Xue and Zhu and does not state that the general assertion has been resolved.