  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-Poincare 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-Poincare series.
