Illinois Journal of Mathematics
- Illinois J. Math.
- Volume 55, Number 4 (2011), 1267-1297.
Irreducible vector-valued modular forms of dimension less than six
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.
Illinois J. Math., Volume 55, Number 4 (2011), 1267-1297.
First available in Project Euclid: 12 July 2013
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Marks, Christopher. Irreducible vector-valued modular forms of dimension less than six. Illinois J. Math. 55 (2011), no. 4, 1267--1297. doi:10.1215/ijm/1373636684. https://projecteuclid.org/euclid.ijm/1373636684