  For an $L^2$-normalized holomorphic newform $f$ of weight $k$ on a hyperbolic
surface of volume $V$ attached to an Eichler order of squarefree level in an
indefinite quaternion algebra over $\mathbb{Q}$, we prove the sup-norm estimate
  \[
  \| \Im(\cdot)^{\frac{k}{2}} f \|_{\infty} \ll_{\epsilon} (k
V)^{\frac{1}{4}+\epsilon}
  \] with absolute implied constant. For a cuspidal Maa{\ss} newform $\varphi$
of eigenvalue $\lambda$ on such a surface, we prove that
  \[
  \|\varphi \|_{\infty} \ll_{\lambda,\epsilon} V^{\frac{1}{4}+\epsilon}.
  \]
  We establish analogous estimates in the setting of definite quaternion
algebras.
