  Using the language of vertex operator algebras (VOAs) and vector-valued
modular forms we study the modular group representations and spaces of 1-point
functions associated to intertwining operators for Virasoro minimal model VOAs.
We examine all representations of dimension less than four associated to
irreducible modules for minimal models, and determine when the kernel of these
representations is a congruence or noncongruence subgroup of the modular group.
Arithmetic criteria are given on the indexing of the irreducible modules for
minimal models that imply the associated modular group representation has a
noncongruence kernel, independent of the dimension of the representation. The
algebraic structure of the spaces of 1-point functions for intertwining
operators is also studied, via a comparison with the associated spaces of
holomorphic vector-valued modular forms.
