  Let $\mathcal{O}$ be a maximal order in the quaternion algebra over
$\mathbb{Q}$ ramified at $p$ and $\infty$. We prove two theorems that allow us
to recover the structure of $\mathcal{O}$ from limited information. The first
says that for any infinite set $S$ of integers coprime to $p$, $\mathcal{O}$ is
spanned as a $\mathbb{Z}$-module by elements with norm in $S$. The second says
that $\mathcal{O}$ is determined up to isomorphism by its theta function.
