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 cusp 2,N 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 .
We present an algorithm to compute all Borcherds product paramodular cusp forms of a specified weight and level, describing its implementation in some detail and giving examples of its use.
Abstract. We compute Hecke eigenform bases of spaces of level one, degree three Siegel modular forms and 2-Euler factors of the eigenforms through weight 22. Our method uses the Fourier coefficients of Siegel Eisenstein series, which are fully known and computationally tractable by the work of H. Katsurada; we also use P. Garrett's decomposition of the pullback of the Eisenstein series through the Witt map. Our results support I. Miyawaki's conjectural lift, and they give examples of eigenforms that are congruence neighbors.
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