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 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.

中文翻译：

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来自椭圆曲线的超模形式

非CM椭圆曲线有提升 $乙/\mathbb{问}$到由对称立方体贴图给出的阶数为 2 和权重为 3的准模形式f。我们根据E的 Weierstrass 方程的系数找到f的水平。为了计算超模水平，我们使用局部表示的可用描述$\mathrm{GL}(2,{\mathbb{问}}_p)$附在E上$p\ge 5$ 并确定本地代表 $\mathrm{GL}(2,{\mathbb{问}}_3)$附加到E。