5 problems

Non-eigenform conjecture. If

Let $m\geq 2$ be fixed, and let $f$ be a normalized Hecke eigenform of level one. Its $m$-th Fourier coefficient is the coefficient of $q^m$ in its normalized Fourier expansion. Xu…

Weight-aspect sup-norm conjecture. If $F$ is an eigenfunction of all Hecke operators, then as $k\to\infty$,

Let $F$ range over totally real number fields of degree $n$, let $\mathfrak{n}$ range over non-zero integral ideals of $F$, and let $f$, $g$, and $h$ be Hecke eigenforms of level…

Let $p$) be a prime such that the space $S_3(\Gamma_p^{+})$ of antisymmetric paramodular cusp forms of weight $3$ is one dimensional. In this situation, the unique form gives a new…