Exceptional Congruences for Eta-quotient newforms
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arXiv
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| Format: | Preprint |
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2025
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| _version_ | 1866909915378876416 |
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| author | O'Sullivan, Eddie Stone, Henry Swati Jin, Xiaolan |
| author_facet | O'Sullivan, Eddie Stone, Henry Swati Jin, Xiaolan |
| contents | In 1973, Swinnerton-Dyer completely classified all congruences for coefficients of normalized eigenforms in weights $k \in \{12, 16, 18, 20, 22, 26\}$ on $Γ_{0}(1) = \operatorname{SL}_{2}(\mathbb{Z})$ using the theory of modular Galois representations. In this paper, we classify congruences of Type I and Type II considered by Swinnerton-Dyer for the coefficients of eta-quotient newforms in $S_{k}(N, χ)$. When $k \geq 2$, we prove them using the theory of modular forms modulo primes. We also prove extensions of these congruences modulo prime powers. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2511_16039 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Exceptional Congruences for Eta-quotient newforms O'Sullivan, Eddie Stone, Henry Swati Jin, Xiaolan Number Theory 11F11, 11F33 In 1973, Swinnerton-Dyer completely classified all congruences for coefficients of normalized eigenforms in weights $k \in \{12, 16, 18, 20, 22, 26\}$ on $Γ_{0}(1) = \operatorname{SL}_{2}(\mathbb{Z})$ using the theory of modular Galois representations. In this paper, we classify congruences of Type I and Type II considered by Swinnerton-Dyer for the coefficients of eta-quotient newforms in $S_{k}(N, χ)$. When $k \geq 2$, we prove them using the theory of modular forms modulo primes. We also prove extensions of these congruences modulo prime powers. |
| title | Exceptional Congruences for Eta-quotient newforms |
| topic | Number Theory 11F11, 11F33 |
| url | https://arxiv.org/abs/2511.16039 |