### Symmetry, Integrability and Geometry: Methods and Applications (SIGMA)

SIGMA 14 (2018), 071, 17 pages      arXiv:1712.02437      https://doi.org/10.3842/SIGMA.2018.071
Contribution to the Special Issue on Modular Forms and String Theory in honor of Noriko Yui

### The Chevalley-Weil Formula for Orbifold Curves

Luca Candelori
Department of Mathematics, University of Hawaii at Manoa, Honolulu, HI, USA

Received December 08, 2017, in final form July 02, 2018; Published online July 17, 2018

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.

Key words: orbifold curves; automorphisms; modular curves; Fermat curves.

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