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Fourier Coefficients of Vector-valued Modular Forms of Dimension 2

Published online by Cambridge University Press:  20 November 2018

Cameron Franc  and
Geoffrey Mason
Cameron Franc
Affiliation:
Department of Mathematics, University of California, Santa Cruz e-mail: cfranc@ucsc.edugem@ucsc.edu
Geoffrey Mason
Affiliation:
Department of Mathematics, University of California, Santa Cruz e-mail: cfranc@ucsc.edugem@ucsc.edu
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Abstract

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We prove the following theorem. Suppose that $F\,=\,\left( {{f}_{1}},\,{{f}_{2}} \right)$ is a 2-dimensional, vector-valued modular form on $\text{S}{{\text{L}}_{2}}\left( \mathbb{Z} \right)$ 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.

Keywords

11F4111G99vector-valued modular formmodular groupbounded denominators
Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 57 , Issue 3 , 01 September 2014 , pp. 485 - 494
Copyright
Copyright © Canadian Mathematical Society 2014

References

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