Let \(\Sigma\) be a Seifert homology 3-sphere. Let \(C_ \rho\) be an irreducible flat \(SU(2)\)-connection over \(\Sigma\) associated to the holonomy representation \(\rho\). The article gives a formula for its Floer index modulo 8 in the Floer chain complex if one uses specific Riemannian metrics on \(\Sigma\). By definition this is given by the spectral flow of a family of twisted signature operators coming from a path connecting the given connection to the trivial one. The index is given by the formula: \[ FI(C_ \rho)=2\cdot \sum^{\omega-1}_{k=0}(\Delta_{2(k- \omega)+r}-\Delta_{2k+r})-2n_ 0, \] where \(\omega\), \(n_ 0\) and \(\Delta_ i\) are certain integers coming from the Seifert invariants and the representation \(\rho\) and the dimensions of spaces of \(\pi_ 1(\Sigma)\)-automorphic functions. In particular the Floer index is always even. The computations of Fintushel and Stern can be rediscovered from this theorem. The proof of the result is based on a direct computation of the flow.