  Given a compact Riemann surface $X$ of genus at least $2$ with automorphism
group $G$ we provide formulae that enable us to compute traces of automorphisms
of X on the space of global sections of $G$-linearized line bundles defined on
certain blow-ups of proyective spaces along the curve $X$. The method is an
adaptation of one used by Thaddeus to compute the dimensions of those spaces.
In particular we can compute the traces of automorphisms of $X$ on the Verlinde
spaces corresponding to the moduli space $SU_{X}(2,\xi)$ when $\xi$ is a line
bundle $G$-linearized of suitable degree.
