Decomposing representations of finite groups on Riemann-Roch spaces

If $G$ is a finite subgroup of the automorphism group of a projective curve $X$ and $D$ is a divisor on $X$ stabilized by $G$, then we compute a simplified formula for the trace of the natural representation of $G$ on the Riemann-Roch space $L(D)$, under the assumption that $L(D)$ is ``rational'', $D$ is nonspecial, and the characteristic is ``good''. We discuss the partial formulas that result if $L(D)$ is not rational.