In a closed-shell self-consistent field calculation on a molecule without symmetry the number of degrees of variational freedom is equal to the product of the dimensions of occupied and virtual spaces. It is shown that this relation also applies within each irreducible representation in the case where the molecule has symmetry, and that it can be generalized to open-shell and many-shell cases. Illustrative examples for large, highly symmetric molecules show that extensive variational freedom can persist even in minimal basis sets.