  The l-adic parabolic cohomology groups attached to noncongruence subgroups of
SL_2(Z) are finite-dimensional representations of Gal(Qbar/F) for some number
field F. We exhibit examples (with F=Q) giving rise to Galois representations
whose images are open subgroups of the full group of symplectic similitudes (of
arbitrary dimension). The determination of the image of the Galois group relies
on Katz's classification theorem for reductive subalgebras of gl(N) containing
a principal nilpotent element; the paper also contains a short conceptual proof
of this theorem, suggested by I. Gronowski.
