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arXiv · 2511.13966

Hecke Eigenvalue Equidistribution over the Newspaces with Nebentypus

Erick Ross
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Abstract

Fix a prime $p$, and let $\widehat T_p^{\mathrm{new}}(N,k,\chi) := \chi(p)^{-1/2} p^{-(k-1)/2} T_p^{\mathrm{new}}(N,k,\chi)$ denote the normalized $p$'th Hecke operator over the newspace with nenbentypus $S_k^{\mathrm{new}}(N,\chi)$. In this paper, we determine the distribution of the eigenvalues of $\widehat T_p^{\mathrm{new}}(N,k,\chi)$ as $N+k \to \infty$.

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Erick Ross. 2025-11-17. Hecke Eigenvalue Equidistribution over the Newspaces with Nebentypus. https://arxiv.org/abs/2511.13966

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