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arXiv · 1901.02115

Paramodular forms coming from elliptic curves

Manami Roy
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Abstract

There is a lifting from a non-CM elliptic curve $E/\mathbb{Q}$ to a paramodular form $f$ of degree $2$ and weight $3$ given by the symmetric cube map. We find the level of $f$ in an explicit way in terms of the coefficients of the Weierstrass equation of $E$. In order to compute the paramodular level, we use the available description of the local representations of $\mathrm{GL}(2,\mathbb{Q}_p)$ attached to $E$ for $p \ge 5$ and determine the local representation of $\mathrm{GL}(2,\mathbb{Q}_3)$ attached to $E$.

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Manami Roy. 2019-01-08. Paramodular forms coming from elliptic curves. https://doi.org/10.1016/j.jnt.2021.06.007

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