Structure theorems for vector valued Siegel modular forms of degree 2 and weight \(\det^k \otimes \mathrm{Sym}(10)\). (English) Zbl 1417.11068
Summary: We prove the explicit structure theorems of modules \(\bigoplus_k M_{\det^k \otimes \mathrm{Sym}(10)}(Sp_2(\mathbb{Z}_2))\) of vector valued Siegel modular forms of degree 2, where \(k\) runs over the set of even integers or odd integers. We also check the conjecture given by T. Ibukiyama [Comment. Math. Univ. St. Pauli 61, No. 1, 51–75 (2012; Zbl 1287.11064)] for modules of vector valued Siegel modular forms of degree 2 of weights \(\det^\ast \otimes \mathrm{Sym}(8)\) and \(\det^\ast \otimes \mathrm{Sym}(10)\).
MSC:
| 11F46 | Siegel modular groups; Siegel and Hilbert-Siegel modular and automorphic forms |
| 11F11 | Holomorphic modular forms of integral weight |
Keywords:
structure theorems of modular forms; vector valued Siegel modular forms; determinant of Siegel modular formsCitations:
Zbl 1287.11064References:
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