The Chevalley-Weil Formula for Orbifold Curves

Abstract

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.