On vector valued Siegel modular forms of degree 2 with small levels
type: Item
instance of: scholarly article
title: On vector valued Siegel modular forms of degree 2 with small levels
zbMATH Open document ID: 1256.11033
author: Hiroki Aoki
published in: Osaka Journal of Mathematics
publication date: 2012-11-28T00:00:00Z
full work available at URL: https://projecteuclid.org/euclid.ojm/1350306590
review text: Let \(\Gamma=\Gamma_0(N) \subseteq \text{Sp}_2(\mathbb{Z})\) (genus \(2\)) for \(N=2,3\) or \(4\), and consider the space \[ A_{*,2}(\Gamma) = \oplus_{k\in\mathbb{Z}} A_{k,2}(\Gamma), \] where \(A_{k,2}(\Gamma)\) is the space of Siegel modular forms of weight \(\rho = \text{Sym}^2 \otimes \det^k\). The main result of this paper is that \(A_{*,2}(\Gamma)\) is generated by ten specific modular forms, and that these generators can be constructed by differential operators.
Mathematics Subject Classification ID: 11F46
Mathematics Subject Classification ID: 11F60
zbMATH DE Number: 6110919
zbMATH Keywords: vector valued Siegel modular forms
zbMATH Keywords: generators
reviewed by: Anke D. Pohl
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 6110919