Two properties of symmetric cube transfers of modular forms
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arXiv
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| Format: | Preprint |
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2023
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| _version_ | 1866914508092473344 |
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| author | Banerjee, Debargha Mandal, Tathagata Mondal, Sudipa |
| author_facet | Banerjee, Debargha Mandal, Tathagata Mondal, Sudipa |
| contents | In this article, we study two important properties of ${\rm{sym}}^3$ transfers of the automorphic representation $π$ associated to a modular form. First we compute the conductor of ${\rm{sym}}^3(π)$. Then we detect the types of local automorphic representations at bad primes by the variation of the epsilon factors of symmetric cube transfer of the representation $π$ attached to a cusp form $f$. Here we twist the modular forms by a specific quadratic character. From this variation number, for each prime $p$, we classify all possible types of symmetric cube transfers of the local representations $π_p$. For ${\rm{sym}}^3$ transfer, the most difficult prime is $p=3$. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2304_14555 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Two properties of symmetric cube transfers of modular forms Banerjee, Debargha Mandal, Tathagata Mondal, Sudipa Number Theory In this article, we study two important properties of ${\rm{sym}}^3$ transfers of the automorphic representation $π$ associated to a modular form. First we compute the conductor of ${\rm{sym}}^3(π)$. Then we detect the types of local automorphic representations at bad primes by the variation of the epsilon factors of symmetric cube transfer of the representation $π$ attached to a cusp form $f$. Here we twist the modular forms by a specific quadratic character. From this variation number, for each prime $p$, we classify all possible types of symmetric cube transfers of the local representations $π_p$. For ${\rm{sym}}^3$ transfer, the most difficult prime is $p=3$. |
| title | Two properties of symmetric cube transfers of modular forms |
| topic | Number Theory |
| url | https://arxiv.org/abs/2304.14555 |