Distinguishing newforms

by S. Chow,A. Ghitza

*Int. J. Number Theory* **11**, no. 3 (2015), 893-908.

We study the number of initial Fourier coefficients necessary to distinguish newforms of fixed level and weight.

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 $N$.