Congruence relations for Siegel modular forms of weight 47, 71, and 89. (English) Zbl 1311.11031
Summary: Let \(X_{35}\) be the Siegel cusp form of degree two and weight 35. In [S. Nagaoka et al. “Note on Igusa’s cusp form of weight 35”, to appear in Rocky Mt. J. Math.], the authors proved that \((\operatorname{det} T)a(X_{35}; T) \equiv 0\) mod 23, for every half-integral symmetric matrix \(T\), where \(a(X_{35}; T)\) is the \(T\)th Fourier coefficient of \(X_{35}\). In this paper, we prove that there exist higher-weight examples of this type of congruence.
MSC:
| 11F33 | Congruences for modular and \(p\)-adic modular forms |
| 11F46 | Siegel modular groups; Siegel and Hilbert-Siegel modular and automorphic forms |
References:
| [1] | Andrianov [Andrianov and Zhuravlev 95] A., Modular Forms and Hecke Operators (1995) |
| [2] | DOI: 10.1142/S0129167X05002837 · Zbl 1068.11030 · doi:10.1142/S0129167X05002837 |
| [3] | DOI: 10.1007/s00208-007-0081-7 · Zbl 1171.11029 · doi:10.1007/s00208-007-0081-7 |
| [4] | DOI: 10.2307/2372812 · Zbl 0133.33301 · doi:10.2307/2372812 |
| [5] | DOI: 10.2307/2373943 · Zbl 0415.14026 · doi:10.2307/2373943 |
| [6] | DOI: 10.1007/BF01360845 · Zbl 0086.06701 · doi:10.1007/BF01360845 |
| [7] | DOI: 10.1007/BF01456941 · Zbl 0505.10013 · doi:10.1007/BF01456941 |
| [8] | Kikuta [Nagaoka et al. 14] T., Rocky Mountain Journal of Mathematics (2014) |
| [9] | DOI: 10.1007/978-3-540-37802-0_1 · doi:10.1007/978-3-540-37802-0_1 |
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