Automorphism group characters (reviewed)

If $G$ is a group acting on a curve $X/\C$ of genus $g$, the induced action of $G$ on the $g$-dimensional $\C$-vector space of holomorphic differentials of $X$ gives rise to a representation of $G$. The group algebra decomposition of the Jacobian of $X$ into a product $A_1^{e_1}\times \cdots\times A_r^{e_r}$ of powers of $r$ abelian varieties gives rise to $r$ irreducible subrepresentations of $G$, each of which has an associated character.

The character of each of these representations is identified by its index in the character table for $G$ as listed by Magma (which may differ from GAP).