Eigenspaces of Newforms with Nontrivial Character

Markos Karameris

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arXiv · 2307.07804

Eigenspaces of Newforms with Nontrivial Character

Markos Karameris

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Abstract

Let $S_{k}(\Gamma_0(N),\chi)$ denote the space of holomorphic cuspforms with Dirichlet character $\chi$ and modular subgroup $\Gamma_0(N)$. We will characterize the space of newforms $S_{k}^{new}(\Gamma_0(N),\chi)$ as the intersection of eigenspaces of a particular family of Hecke operators, generalizing the work of Baruch-Purkait to forms with non-trivial character. We achieve this by obtaining representation theoretic results in the $p$-adic case which we then de-adelizize into relations of classical Hecke operators.

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Markos Karameris. 2023-07-15. Eigenspaces of Newforms with Nontrivial Character. https://arxiv.org/abs/2307.07804

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