Distinguishing eigenforms modulo a prime ideal
S. Chow, A. Ghitza
Funct. Approx. Comment. Math. 51, no. 2 (2014), 363-377.
Let $n_0(N,k)$ be the number of initial Fourier coefficients necessary to distinguish newforms of level $N$ and even weight $k$. We produce extensive data to support our conjecture that if $N$ is a fixed squarefree positive integer and $k$ is large then $n_0(N,k)$ is the least prime that does not divide $N$.