Supnorm of an eigenfunction of finitely many Hecke operators

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 fixed finite collection of primes, we prove an L-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 Berard (Math Z 155: 249-276, 1977) to improve the Archimedean amplification.