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| Main Author: | |
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| Format: | Preprint |
| Published: |
2023
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2307.07804 |
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| _version_ | 1866911944756166656 |
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| author | Karameris, Markos |
| author_facet | Karameris, Markos |
| contents | Let $S_{k}(Γ_0(N),χ)$ denote the space of holomorphic cuspforms with Dirichlet character $χ$ and modular subgroup $Γ_0(N)$. We will characterize the space of newforms $S_{k}^{new}(Γ_0(N),χ)$ 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2307_07804 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Eigenspaces of Newforms with Nontrivial Character Karameris, Markos Number Theory Representation Theory 11F11, 11F33, 20C08, 11F25 Let $S_{k}(Γ_0(N),χ)$ denote the space of holomorphic cuspforms with Dirichlet character $χ$ and modular subgroup $Γ_0(N)$. We will characterize the space of newforms $S_{k}^{new}(Γ_0(N),χ)$ 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. |
| title | Eigenspaces of Newforms with Nontrivial Character |
| topic | Number Theory Representation Theory 11F11, 11F33, 20C08, 11F25 |
| url | https://arxiv.org/abs/2307.07804 |