The ring of paramodular cusp forms $S_k(K(p))$ (awaiting review)

The ring of paramodular cusp forms $S_*(K(p))$ for $p$ prime.

The dimensions of weight 2 paramodular cusp forms $S_2(K(p)$ for primes $p<600$ (with the exceptions of 349, 353, 389, 461, 523, 587) have been computed by C. Poor and D. S. Yuen [arXiv:1004.4699]. Poor and Yuen also prove that any weight 2 nonlifts in this range of primes ($ p < 600 $) can occur only at primes 277, 349, 353, 389, 461, 523, 587. The nonlift weight 2 eigenform at $p=277$ is known and proved; the others are conjectured.

Dimension formulas for paramodular cusp forms $S_k(K(p))$ for $p$ prime for weights 3 and higher were proven by Tomoyoshi Ibukiyama in Dimension formulas of Siegel modular forms of weight 3 and supersingular abelian surfaces, Siegel Modular Forms and Abelian Varieties, Proceedings of the 4th Spring Conference on Modular Forms and Related Topics, Ryushido, Kobe, 2007.