  We use Maeda's Conjecture to prove that the Rankin-Cohen bracket of an
eigenform and any modular form is only an eigenform when forced to be because
of the dimensions of the underlying spaces. We further determine when the
Rankin-Cohen bracket of an eigenform and modular form is not forced to produce
an eigenform and when it is determined by the injectivity of the operator
itself. This can also be interpreted as using the Rankin-Cohen bracket operator
of eigenforms to create evidence for Maeda's Conjecture.

Number Theory