3 problems

Let $k$ be such that the indicated spaces are defined, and let $f \in S_{2k-4}(\operatorname{SL}_2(\mathbb{Z}))$ and $g \in S_k(\operatorname{SL}_2(\mathbb{Z}))$ be normalized Heck…

Let $F$ be a totally real number field, let $\psi$ be a non-trivial unitary character of $\mathbb{A}/F$, and fix a totally positive $\xi\in F^\times$. Let $\pi$ be an irreducible r…

Let $k$ be positive and even, let $f \in S_{2k-2(n+r)}(\operatorname{SL}_2(\mathbb{Z}))$ be a normalized Hecke eigenform, let $F^{(2n+2r)}$ be its Ikeda lift, and let…