  Associated to an open subgroup $G$ of $\GL_2(\Zhat)$ satisfying conditions
$-I \in G$ and $\det(G) \subsetneq (\Zhat)^{\times}$ there is a modular curve
$X_G$ which is a smooth compact curve defined over an extension of $\Q.$ In
this article, we give a complete list of all such prime power level genus $0$
modular curves with a point.
