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 be an irreducible representation of the modular group such that has finite order . We study holomorphic vector-valued modular forms of integral weight associated to which have *rational* Fourier coefficients. (These span the complex space of all integral weight vector-valued modular forms associated to .) As a special case of the main theorem, we prove that if does *not* divide , then every nonzero 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