  In the 1930s Chevalley and Weil gave a formula for decomposing the canonical
representation on the space of differential forms of the Galois group of a
ramified Galois cover of Riemann surfaces. In this article we prove an
analogous Chevalley-Weil formula for ramified Galois covers of orbifold curves.
We then specialize the formula to the case when the base orbifold curve is the
(reduced) modular orbifold. As an application of this latter formula we
decompose the canonical representations of modular curves of full, prime level
and of Fermat curves of arbitrary exponent.
