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arXiv · 2304.14555

Two properties of symmetric cube transfers of modular forms

Debargha Banerjee·Tathagata Mandal·Sudipa Mondal
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Abstract

In this article, we study two important properties of ${\rm{sym}}^3$ transfers of the automorphic representation $\pi$ associated to a modular form. First we compute the conductor of ${\rm{sym}}^3(\pi)$. 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 $\pi$ 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 $\pi_p$. For ${\rm{sym}}^3$ transfer, the most difficult prime is $p=3$.

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Debargha Banerjee, Tathagata Mandal, Sudipa Mondal. 2023-04-27. Two properties of symmetric cube transfers of modular forms. https://doi.org/10.1016/j.jnt.2024.12.013

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