Quantitative level lowering for weight two Hilbert modular forms
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arXiv
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| Format: | Preprint |
| Publié: |
2024
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| _version_ | 1866910580731805696 |
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| author | Moakher, Mohamed |
| author_facet | Moakher, Mohamed |
| contents | We generalize a result of Ribet and Takahashi on the parametrization of elliptic curves by Shimura curves to the Hilbert modular setting. In particular, we study the behaviour of the parametrization of modular abelian varieties by Shimura curves associated to quaternion algebras $D$ over a totally real field $F$, as we vary $D$. As a consequence, we obtain that on these Shimura curves, the cohomological congruence module is equal to the ring theoretic congruence module even in cases where we do not have multiplicity one, thereby extending results of Manning and Böckle-Khare-Manning. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2408_15410 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Quantitative level lowering for weight two Hilbert modular forms Moakher, Mohamed Number Theory Primary 11F33, Secondary 11F80, 11G10 We generalize a result of Ribet and Takahashi on the parametrization of elliptic curves by Shimura curves to the Hilbert modular setting. In particular, we study the behaviour of the parametrization of modular abelian varieties by Shimura curves associated to quaternion algebras $D$ over a totally real field $F$, as we vary $D$. As a consequence, we obtain that on these Shimura curves, the cohomological congruence module is equal to the ring theoretic congruence module even in cases where we do not have multiplicity one, thereby extending results of Manning and Böckle-Khare-Manning. |
| title | Quantitative level lowering for weight two Hilbert modular forms |
| topic | Number Theory Primary 11F33, Secondary 11F80, 11G10 |
| url | https://arxiv.org/abs/2408.15410 |