Dimension formulas for Siegel modular forms of level 4

IF 0.8 3区数学 Q2 MATHEMATICS

Mathematika Pub Date : 2023-05-31 DOI:10.1112/mtk.12207

Manami Roy, Ralf Schmidt, Shaoyun Yi

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引用次数: 2

Abstract

We prove several dimension formulas for spaces of scalar-valued Siegel modular forms of degree 2 with respect to certain congruence subgroups of level 4. In case of cusp forms, all modular forms considered originate from cuspidal automorphic representations of $GSp (4, A)$ whose local component at $p = 2$ admits nonzero fixed vectors under the principal congruence subgroup of level 2. Using known dimension formulas combined with dimensions of spaces of fixed vectors in local representations at $p = 2$ , we obtain formulas for the number of relevant automorphic representations. These, in turn, lead to new dimension formulas, in particular for Siegel modular forms with respect to the Klingen congruence subgroup of level 4.

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四阶Siegel模形式的维数公式

我们证明了关于4阶同余子群的2阶标量值Siegel模形式空间的几个维度公式。对于尖形形式，所考虑的所有模形式都源于GSp(4,A)${\rm GSp}(4，{\mathbb {A}})$的尖形自同构表示，其局部分量在p=2$p=2$处允许在第2层主同余子群下的非零固定向量。利用已知的维数公式，结合p=2$p=2$局部表示中固定向量空间的维数，得到了相关自同构表示个数的公式。这些，反过来，导致新的维度公式，特别是关于第4层克林根同余子群的西格尔模形式。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Mathematika MATHEMATICS, APPLIED-MATHEMATICS

CiteScore

1.40

自引率

0.00%

发文量

审稿时长

>12 weeks

期刊介绍： Mathematika publishes both pure and applied mathematical articles and has done so continuously since its founding by Harold Davenport in the 1950s. The traditional emphasis has been towards the purer side of mathematics but applied mathematics and articles addressing both aspects are equally welcome. The journal is published by the London Mathematical Society, on behalf of its owner University College London, and will continue to publish research papers of the highest mathematical quality.