  We compute the spectral action of $SU(2)/\Gamma$ with the trivial spin
structure and the round metric and find it in each case to be equal to
$\frac{1}{|\Gamma|} (\Lambda^3 \hat{f}^{(2)}(0) - 1/4\Lambda \hat{f}(0))+
O(\Lambda^{-\infty})$. We do this by explicitly computing the spectrum of the
Dirac operator for $SU(2)/\Gamma$ equipped with the trivial spin structure and
a selection of metrics. Here $\Gamma$ is a finite subgroup of SU(2). In the
case where $\Gamma$ is cyclic, or dicyclic, we consider the one-parameter
family of Berger metrics, which includes the round metric, and when $\Gamma$ is
the binary tetrahedral, binary octahedral or binary icosahedral group, we only
consider the case of the round metric.
