  Let $\phi$ be a Laplace eigenfunction on a compact hyperbolic surface
attached to an order in a quaternion algebra. Assuming that $\phi$ is an
eigenfunction of Hecke operators at a \emph{fixed finite} collection of primes,
we prove an $L^\infty$-norm bound for $\phi$ that improves upon the trivial
estimate by a power of the logarithm of the eigenvalue. We have constructed an
amplifier whose length depends on the support of the amplifier on Hecke trees.
We have used a method of B\'erard in \cite{Be} to improve the archimedean
amplification.
