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Winter 2011 Irreducible vector-valued modular forms of dimension less than six
Christopher Marks
Illinois J. Math. 55(4): 1267-1297 (Winter 2011). DOI: 10.1215/ijm/1373636684


An algebraic classification is given for spaces of holomorphic vector-valued modular forms of arbitrary real weight and multiplier system, associated to irreducible, $T$-unitarizable representations of the full modular group, of dimension less than six. For representations of dimension less than four, it is shown that the associated space of vector-valued modular forms is a cyclic module over a certain skew polynomial ring of differential operators. For dimensions four and five, a complete list of possible Hilbert–Poincaré series is given, using the fact that the space of vector-valued modular forms is a free module over the ring of classical modular forms for the full modular group. A mild restriction is then placed on the class of representation considered in these dimensions, and this again yields an explicit determination of the associated Hilbert–Poincaré series.


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Christopher Marks. "Irreducible vector-valued modular forms of dimension less than six." Illinois J. Math. 55 (4) 1267 - 1297, Winter 2011.


Published: Winter 2011
First available in Project Euclid: 12 July 2013

zbMATH: 1343.11052
MathSciNet: MR3082869
Digital Object Identifier: 10.1215/ijm/1373636684

Primary: 11F03, 11F99

Rights: Copyright © 2011 University of Illinois at Urbana-Champaign


Vol.55 • No. 4 • Winter 2011
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