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arXiv · 1612.00925

Siegel Paramodular Forms of Weight 2 and Squarefree Level

Cris Poor·Jerry Shurman·David S. Yuen
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Abstract

We compute the space $S_2(K(N))$ of weight $2$ Siegel paramodular cusp forms of squarefree level $N<300$. In conformance with the paramodular conjecture of A. Brumer and K. Kramer, the space is only the additive (Gritsenko) lift space of the Jacobi cusp form space $J_{2,N}^{\text{cusp}}$ except for $N=249,295$, when it further contains one nonlift newform. For these two values of $N$, the Hasse-Weil $p$-Euler factors of a relevant abelian surface match the spin $p$-Euler factors of the nonlift newform for the first two primes $p\nmid N$.

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Cris Poor, Jerry Shurman, David S. Yuen. 2016-12-03. Siegel Paramodular Forms of Weight 2 and Squarefree Level. https://doi.org/10.1142/s1793042117501469

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