Congruences and ramified primes in fields of coefficients of newforms
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arXiv
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| Auteurs principaux: | , |
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| Format: | Preprint |
| Publié: |
2026
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| _version_ | 1866908924799614976 |
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| author | Freitas, Nuno Gawron, Filip |
| author_facet | Freitas, Nuno Gawron, Filip |
| contents | We investigate the splitting behavior of $\ell$ in the coefficient field of a newform $f$ of level $N$, under the assumption that $f$ is congruent modulo a prime above $\ell$ to another newform $g$ whose level divides $N/p^2$ for some prime $p\mid N$. In particular, we show that the maximal real subfield of the $\ell$-th cyclotomic field, $\mathbb{Q}(ζ_\ell + ζ_\ell^{-1})$, is contained in the coefficient field of $f$. We conclude by presenting explicit examples that illustrate these results. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2603_29468 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Congruences and ramified primes in fields of coefficients of newforms Freitas, Nuno Gawron, Filip Number Theory We investigate the splitting behavior of $\ell$ in the coefficient field of a newform $f$ of level $N$, under the assumption that $f$ is congruent modulo a prime above $\ell$ to another newform $g$ whose level divides $N/p^2$ for some prime $p\mid N$. In particular, we show that the maximal real subfield of the $\ell$-th cyclotomic field, $\mathbb{Q}(ζ_\ell + ζ_\ell^{-1})$, is contained in the coefficient field of $f$. We conclude by presenting explicit examples that illustrate these results. |
| title | Congruences and ramified primes in fields of coefficients of newforms |
| topic | Number Theory |
| url | https://arxiv.org/abs/2603.29468 |