Chow's stability conjecture for holomorphic newforms

Let $q$ be a positive squarefree integer, let $k$ be a positive even integer, and let $n_0(q,k)$ be the least integer such that equality of Hecke eigenvalues at all primes $p\leq n_0(q,k)$ forces two holomorphic newforms of weight $k$, level $q$, and principal character to be equal. Chow's stability conjecture. There exists a positive integer $k_0$ such that for all $k\geq k_0$, $n_0(q,k)$ is the smallest prime not dividing $q$. The conjecture is based on numerical calculations for many small squarefree levels; the source gives no resolution.