Traces of Hecke operators on Drinfeld modular forms for $\mathrm{GL}_2(\mathbb{F}_q[T])$
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arXiv
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| Format: | Preprint |
| Veröffentlicht: |
2024
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| _version_ | 1866918361746636800 |
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| author | de Vries, Sjoerd |
| author_facet | de Vries, Sjoerd |
| contents | In this paper, we study traces of Hecke operators on Drinfeld modular forms of level 1 in the case $A = \mathbb{F}_q[T]$. We deduce closed-form expressions for traces of Hecke operators corresponding to primes of degree at most 2 and provide algorithms for primes of higher degree. We improve the Ramanujan bound and deduce the decomposition of cusp forms of level $Γ_0(\mathfrak{p})$ into oldforms and newforms, as conjectured by Bandini-Valentino, under the hypothesis that each Hecke eigenvalue has multiplicity less than $p$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2407_04555 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Traces of Hecke operators on Drinfeld modular forms for $\mathrm{GL}_2(\mathbb{F}_q[T])$ de Vries, Sjoerd Number Theory Algebraic Geometry 11F52, 11F72 (Primary) 11G09, 11R65 (Secondary) In this paper, we study traces of Hecke operators on Drinfeld modular forms of level 1 in the case $A = \mathbb{F}_q[T]$. We deduce closed-form expressions for traces of Hecke operators corresponding to primes of degree at most 2 and provide algorithms for primes of higher degree. We improve the Ramanujan bound and deduce the decomposition of cusp forms of level $Γ_0(\mathfrak{p})$ into oldforms and newforms, as conjectured by Bandini-Valentino, under the hypothesis that each Hecke eigenvalue has multiplicity less than $p$. |
| title | Traces of Hecke operators on Drinfeld modular forms for $\mathrm{GL}_2(\mathbb{F}_q[T])$ |
| topic | Number Theory Algebraic Geometry 11F52, 11F72 (Primary) 11G09, 11R65 (Secondary) |
| url | https://arxiv.org/abs/2407.04555 |