Newforms mod p in squarefree level, with applications to Monsky's Hecke-stable filtration
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arXiv
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| Autores principales: | , , |
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| Formato: | Preprint |
| Publicado: |
2018
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| _version_ | 1866910714361282560 |
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| author | Deo, Shaunak V. Medvedovsky, Anna Ghitza, Alexandru |
| author_facet | Deo, Shaunak V. Medvedovsky, Anna Ghitza, Alexandru |
| contents | We propose an algebraic definition of the space of l-new mod-p modular forms for Gamma0(Nl) in the case that l is prime to N, which naturally generalizes to a notion of newforms modulo p in squarefree level. We use this notion of newforms to interpret the Hecke algebras on the graded pieces of the space of mod-2 level-3 modular forms described by Paul Monsky. Along the way, we describe a renormalized version of the Atkin-Lehner involution: no longer an involution, it is an automorphism of the algebra of modular forms, even in characteristic p. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_1808_04588 |
| institution | arXiv |
| publishDate | 2018 |
| record_format | arxiv |
| spellingShingle | Newforms mod p in squarefree level, with applications to Monsky's Hecke-stable filtration Deo, Shaunak V. Medvedovsky, Anna Ghitza, Alexandru Number Theory 11F33 (Primary) 11F30, 11F11, 11F25, 11F23 (Secondary) We propose an algebraic definition of the space of l-new mod-p modular forms for Gamma0(Nl) in the case that l is prime to N, which naturally generalizes to a notion of newforms modulo p in squarefree level. We use this notion of newforms to interpret the Hecke algebras on the graded pieces of the space of mod-2 level-3 modular forms described by Paul Monsky. Along the way, we describe a renormalized version of the Atkin-Lehner involution: no longer an involution, it is an automorphism of the algebra of modular forms, even in characteristic p. |
| title | Newforms mod p in squarefree level, with applications to Monsky's Hecke-stable filtration |
| topic | Number Theory 11F33 (Primary) 11F30, 11F11, 11F25, 11F23 (Secondary) |
| url | https://arxiv.org/abs/1808.04588 |