Level of a Shimura curve (awaiting review)

Let $(O,\mu)$ be a polarized quaternion order, and let $G \colonequals \Aut_{\pm\mu}(O)\ltimes \widehat{O}^\times$ be the corresponding enhanced semidirect product. Let $H \le G$ be an open compact subgroup. The level of $H$ is the least positive integer $N$ such that $H$ contains \[ \ker(\widehat{O}^\times \to \modstar{O}{NO}). \]

The level of a Shimura curve $X_H$ is the level of the corresponding open compact subgroup $H$.