  We study extreme values of desymmetrized eigenfunctions (so called Hecke
eigenfunctions) for the quantized cat map, a quantization of a hyperbolic
linear map of the torus.
  In a previous paper it was shown that for prime values of the inverse Planck
constant N=1/h, such that the map is diagonalizable (but not upper triangular)
modulo N, the Hecke eigenfunctions are uniformly bounded. The purpose of this
paper is to show that the same holds for any prime N provided that the map is
not upper triangular modulo N.
  We also find that the supremum norms of Hecke eigenfunctions are << N^epsilon
for all epsilon>0 in the case of N square free.
