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On the Fourier coefficients of 2-dimensional vector-valued modular forms


Author: Geoffrey Mason
Journal: Proc. Amer. Math. Soc. 140 (2012), 1921-1930
MSC (2010): Primary 11F99
DOI: https://doi.org/10.1090/S0002-9939-2011-11098-0
Published electronically: October 5, 2011
MathSciNet review: 2888179
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Abstract | References | Similar Articles | Additional Information

Abstract: Let $ \rho : SL(2, \mathbb{Z}) \rightarrow GL(2, \mathbb{C})$ be an irreducible representation of the modular group such that $ \rho (T)$ has finite order $ N$. We study holomorphic vector-valued modular forms $ F(\tau )$ of integral weight associated to $ \rho $ which have rational Fourier coefficients. (These span the complex space of all integral weight vector-valued modular forms associated to $ \rho $.) As a special case of the main theorem, we prove that if $ N$ does not divide $ 120$, then every nonzero $ F(\tau )$ has Fourier coefficients with unbounded denominators.


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Additional Information

Geoffrey Mason
Affiliation: Department of Mathematics, University of California, Santa Cruz, Santa Cruz, California 95064
Email: gem@cats.ucsc.edu

DOI: https://doi.org/10.1090/S0002-9939-2011-11098-0
Received by editor(s): September 3, 2010
Received by editor(s) in revised form: February 8, 2011
Published electronically: October 5, 2011
Additional Notes: Supported by NSA and NSF
Communicated by: Kathrin Bringmann
Article copyright: © Copyright 2011 American Mathematical Society

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