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An algebraic classification is given for spaces of holomorphic vector-valuedmodular forms of arbitrary real weight and multiplier system, associated toirreducible, T-unitarizable representations of the full modular group, ofdimension less than six. For representations of dimension less than four, it isshown that the associated space of vector-valued modular forms is a cyclicmodule over a certain skew polynomial ring of differential operators. Fordimensions four and five, a complete list of possible Hilbert-Poincare seriesis given, using the fact that the space of vector-valued modular forms is afree module over the ring of classical modular forms for the full modulargroup. A mild restriction is then placed on the class of representationconsidered in these dimensions, and this again yields an explicit determinationof the associated Hilbert-Poincare series.

Irreducible vector-valued modular forms of dimension less than six