Computations of spaces of paramodular forms of general level
J. Korean Math. Soc. 2016 Vol. 53, No. 3, 645-689
Published online 2016 May 01
Jeffery Breeding II, Cris Poor, and David S. Yuen
Fordham University, Fordham University, Lake Forest University
Abstract : This article gives upper bounds on the number of Fourier-Jacobi coefficients that determine a paramodular cusp form in degree two. The level~N of the paramodular group is completely general throughout. Additionally, spaces of Jacobi cusp forms are spanned by using the theory of theta blocks due to Gritsenko, Skoruppa and Zagier. We combine these two techniques to rigorously compute spaces of paramodular cusp forms and to verify the Paramodular Conjecture of Brumer and Kramer in many cases of low level. The proofs rely on a detailed description of the zero dimensional cusps for the subgroup of integral elements in each paramodular group.
Keywords : paramodular, theta block, Fourier-Jacobi
MSC numbers : 11F46, 11F50
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