Congruence Relations for Siegel Modular Forms of Weight 47, 71, and 89

Abstract

Let X₃₅ be the Siegel cusp form of degree two and weight 35. In [Nagaoka et al. 14], the authors proved that for every half-integral symmetric matrix T, where a(X₃₅; T) is the Tth Fourier coefficient of X₃₅. In this paper, we prove that there exist higher-weight examples of this type of congruence.

Keywords::

• congruence
• theta operator
• Siegel modular forms of odd weights
• Primary 11F33
• Secondary 11F46

ACKNOWLEDGMENTS

The author would like to express his gratitude to Professor S. Böcherer, T. Kikuta, H. Kodama, and Professor S. Nagaoka for useful discussions. The author would like to express his gratitude to Professor T. Ikeda for his helpful advice and encouragement.

Notes

¹The source code for this package can be found at https://github.com/stakemori/degree2.