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Siegel paramodular forms of weight 2 and squarefree level

Cris Poor

Department of Mathematics, Fordham University, Bronx, NY 10458, USA

E-mail Address: [email protected]

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Jerry Shurman

Reed College, Portland, OR 97202, USA

E-mail Address: [email protected]

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, and

David S. Yuen

Department of Mathematics and Computer Science, Lake Forest College, 555 N. Sheridan Rd., Lake Forest, IL 60045, USA

E-mail Address: [email protected]

Corresponding author.

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https://doi.org/10.1142/S1793042117501469Cited by:7 (Source: Crossref)

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 Brumer and Kramer, the space is only the additive (Gritsenko) lift space of the Jacobi cusp form space $J_{2, N}^{cusp}$ 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 $p ∤ N$ .

Keywords:

AMSC: 11F46, 11F55, 11F30, 11F50

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