3 problems

Let $p$ be a prime, let $f$ be the modular form in the construction, let $\widetilde{\mathscr{O}}$ and $\mathscr{O}'$ be the relevant orders, and write … Let…

Let $p$ be the prime and let $f$ be the weight-$2$ eigenform introduced in the construction above. Fix $\sigma\in\{+,-\}$, and let $c_f(d)$ be the coefficient of $q^d$ in … Let…

Let $k$ be a positive integer, $N$ a positive integer, and let $\chi$ be a Dirichlet character modulo $4N$. Suppose that $f\in M_{k+1/2}(4N,\chi)$ is a Hecke eigenform, so that Shi…