  Crossing probabilities for critical 2-D percolation on large but finite
lattices have been derived via boundary conformal field theory. These
predictions agree very well with numerical results. However, their derivation
is heuristic and there is evidence of additional symmetries in the problem.
This contribution gives a preliminary examination some unusual modular behavior
of these quantities. In particular, the derivatives of the "horizontal" and
"horizontal-vertical" crossing probabilities transform as a vector modular
form, one component of which is an ordinary modular form and the other the
product of a modular form with the integral of a modular form. We include
consideration of the interplay between conformal and modular invariance that
arises.
