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Let $D$ be an indefinite quaternion division algebra over $\mathbb{Q}$. Weapproach the problem of bounding the sup-norms of automorphic forms $\phi$ on$D^\times(\mathbb{A})$ that belong to irreducible automorphic representationsand transform via characters of unit groups of orders of $D$. We obtain anon-trivial upper bound for $\|\phi\|_\infty$ in the level aspect that is validfor arbitrary orders. This generalizes and strengthens previously known upperbounds for $\|\phi\|_\infty$ in the setting of newforms for Eichler orders. Inthe special case when the index of the order in a maximal order is a squarefullinteger $N$, our result specializes to $\|\phi\|_\infty \ll_{\pi_\infty,\epsilon} N^{1/3 + \epsilon} \|\phi\|_2$.  A key application of our result is to automorphic forms $\phi$ whichcorrespond at the ramified primes to either minimal vectors (in the sense ofHu-Nelson-Saha), or $p$-adic microlocal lifts (in the sense of Nelson). Forsuch forms, our bound specializes to $\| \phi\|_\infty \ll_{\epsilon}C^{\frac16 + \epsilon}\|\phi\|_2$ where $C$ is the conductor of therepresentation $\pi$ generated by $\phi$. This improves upon the previouslyknown local bound $\|\phi\|_\infty \ll_{\lambda, \epsilon} C^{\frac14 +\epsilon}\|\phi\|_2$ in these cases.

Sup-norms of eigenfunctions in the level aspect for compact arithmetic surfaces