Siegel paramodular forms of weight 2 and squarefree level

摘要

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 inverted iota N.