Fourier coefficients of vector-valued modular forms of dimension 2

We prove the following theorem. Suppose that \(F=(f_1, f_2)\) is a 2-dimensional vector-valued modular form on \(SL_2(Z)\) whose component functions \(f_1, f_2\) have rational Fourier coefficients with bounded denominators. Then \(f_1\) and \(f_2\) are classical modular forms on a congruence subgrou...

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Bibliographic Details
Published in:arXiv.org 2013-04
Main Authors: Cameron, Franc, Mason, Geoffrey
Format: Article
Language:English
Subjects:
Analytic functions
Subgroups
Online Access:Get full text
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Summary:We prove the following theorem. Suppose that \(F=(f_1, f_2)\) is a 2-dimensional vector-valued modular form on \(SL_2(Z)\) whose component functions \(f_1, f_2\) have rational Fourier coefficients with bounded denominators. Then \(f_1\) and \(f_2\) are classical modular forms on a congruence subgroup of the modular group.
ISSN:2331-8422
DOI:10.48550/arxiv.1304.4288