Abstract
AbstractWe construct a ring of meromorphic Siegel modular forms of degree 2 and level 5, with singularities supported on an arrangement of Humbert surfaces, which is generated by four singular theta lifts of weights 1, 1, 2, 2 and their Jacobian. We use this to prove that the ring of holomorphic Siegel modular forms of degree 2 and level $$\Gamma _0(5)$$
Γ
0
(
5
)
is minimally generated by eighteen modular forms of weights 2, 4, 4, 4, 4, 4, 6, 6, 6, 6, 10, 11, 11, 11, 13, 13, 13, 15.
Publisher
Springer Science and Business Media LLC
Subject
Algebra and Number Theory
Reference14 articles.
1. Aoki, H., Ibukiyama, T.: Simple graded rings of Siegel modular forms, differential operators and Borcherds products. Int. J. Math. 16(3), 249–279 (2005)
2. Böcherer, S., Ibukiyama, T.: Surjectivity of Siegel $$\Phi $$-operator for square free level and small weight. Ann. Inst. Fourier (Grenoble) 62(1), 121–144 (2012)
3. Borcherds, R.: Automorphic forms with singularities on Grassmannians. Invent. Math. 132(3), 491–562 (1998)
4. Grayson, D.R., Stillman, M.E.: Macaulay2, a software system for research in algebraic geometry. http://www.math.uiuc.edu/Macaulay2/
5. Gritsenko, V. Fourier–Jacobi functions in $$n$$ variables. Zap. Nauchn. Sem. Leningrad. Otdel. Mat. Inst. Steklov. (LOMI) 168 (Anal. Teor. Chisel i Teor. Funktsiĭ. 9), 32–44, 187–188 (1988)