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Given a compact Riemann surface $X$ of genus at least $2$ with automorphismgroup $G$ we provide formulae that enable us to compute traces of automorphismsof X on the space of global sections of $G$-linearized line bundles defined oncertain blow-ups of proyective spaces along the curve $X$. The method is anadaptation 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 Verlindespaces corresponding to the moduli space $SU_{X}(2,\xi)$ when $\xi$ is a linebundle $G$-linearized of suitable degree.

The Verlinde traces for $\mathcal{SU}_{X}(2,\xi)$ and blow-ups