Nonvanishing of Second Coefficients of Hecke Polynomials on the Newspace

William Cason, Akash Jim, Charlie Medlock +3

For $m\ge 1$, let $N\ge 1$ be coprime to $m$, $k\ge 2$, and $\chi$ be a Dirichlet character modulo $N$ with $\chi (-1)=(-1{)}^k$. Then let $T_m^{\text{new}}(N,k,\chi )$ denote the restric…