Proportion of Atkin-Lehner sign patterns and Hecke Eigenvalue Equidistribution

Erick Ross, Alexandre van Lidth, Martha Rose Wolf +1

Let $N\ge 1$, $k\ge 2$ even, and $\ddot{I}ƒ$ denote a sign pattern for $N$. In this paper, we first determine the exact proportion of forms in $S_k(N)$ and $S_k^{\mathrm{new}}(N)$ with a…