4 problems

Let $k\geq 4$ and let $\ell>k+1$ be prime. Let $N=p_1\cdots p_t$ be squarefree, with distinct prime factors $p_i$, and let $\varepsilon$ be an Atkin-Lehner eigensystem for…

Let $A$ be the coefficient ring and let $T$ be the prime defining the level. For weights $k,l$, write $S_{k,l}(\mathrm{GL}_2(A))$ for the space of Drinfeld cusp forms for…

Atkin–Lehner equidistribution conjecture. For all $k\geq 2$, the space $S_k(\Gamma_0(2))$ decomposes under $W_2$ into Hecke-irreducible subspaces of dimensions $\lfloor d/2\rfloor$…

Let $N\in\mathbb{Z}_{>0}$ be squarefree. Let $S_k^{\mathrm{new}}(\Gamma_0(N))$ be the newspace, and let $T_n$ be a Hecke operator with $n\geq2$ coprime to $N$. Squarefree-level Mae…