8 problems

Let $k$ and $n$ be natural numbers with $k-n$ even. Let $f\in S_{2k}(\Gamma_1)$ be a normalized Hecke eigenform, and let $F_{2n}\in S_{k+n}(\Gamma_{2n})$ be the Ikeda lift of $f$.…

Let $S_{n(\lambda)}(\Gamma[\sqrt{-3}])$ be the space of Picard modular cusp forms of weight $n(\lambda)$, and let $S_{n(\lambda)}^{\rm gen}(\Gamma[\sqrt{-3}])$ denote the proposed…

Let $a$ and $b$ be the parameters occurring in the indicated weights, and let $S^{\chi}_{a+2}(\Gamma_0(9))$ denote the subspace defined using the quadratic character modulo $3$. Th…

Let $a$ and $b$ be the parameters occurring in the indicated weights. The level-3 newform lift conjecture. There should be a lift … with $\mathfrak{S}_4$-representation…

Let $a$ and $b$ be the parameters occurring in the indicated weights. The level-3 minus-space lift conjecture. There should be a lift … with $\mathfrak{S}_4$-representation…

Let $a$ and $b$ be the parameters occurring in the indicated weights, let $f$ be an eigenform in $S^{-}_{a+b+3}(\Gamma_0(9))$, and write $a_p(f)$ for its Hecke eigenvalue. The two-…

Let $a$ and $b$ be the parameters occurring in the indicated weights, and let $S^{-}_{b+2}(\Gamma_0(9))$ be the relevant Fricke-eigenspace of cusp forms. The one-dimensional lift c…

Let $F^{(4)}$ be the degree-four Hermitian modular form of weight $12$ defined by … The form $F^{(4)}$ is nonzero. Hermitian Ikeda-lift conjecture. The form $F^{(4)}$ is a Hermitia…