  We prove a sub-convex estimate for the sup-norm of $L^2$-normalized
holomorphic modular forms of weight $k$ on the upper half plane, with respect
to the unit group of a quaternion division algebra over $\mf Q$. More precisely
we show that when the $L^2$ norm of an eigenfunction $f$ is one, | f |_\infty
\ll k^{1/2 - 12/131 + \varepsilon}, for any $\varepsilon>0$ and for all $k$
sufficiently large.
