  We study the zeros of cusp forms of large weight for the modular group, which
have a very large order of vanishing at infinity, so that they have a fixed
number D of finite zeros in the fundamental domain. We show that for large
weight the zeros of these forms cluster near D vertical lines, with the zeros
of a weight k form lying at height approximately log(k). This is in contrast to
previously known cases, such as Eisenstein series, where the zeros lie on the
circular part of the boundary of the fundamental domain, or the case of
cuspidal Hecke eigenforms where the zeros are uniformly distributed in the
fundamental domain.
  Our method uses the Faber polynomials. We show that for our class of cusp
forms, the associated Faber polynomials, suitably renormalized, converge to the
truncated exponential polynomial of degree D.
