Signs of the Second Coefficients of Hecke Polynomials

Erick Ross, Hui Xue

Let $T_m(N,k,\chi )$ be the $m$-th Hecke operator of level $N$, weight $k\ge 2$, and nebentypus $\chi$, where $N$ is coprime to $m$. We first show that for any given $m\ge 1$, the sec…