Distinguishing eigenforms modulo a prime ideal

by S. Chow,A. Ghitza

*Funct. Approx. Comment. Math.* **51**, no. 2 (2014), 363-377.

We study the number of initial Fourier coefficients necessary to distinguish eigenforms modulo a prime ideal.

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 $N$.