  This paper deals with some questions that have received a lot of attention
since they were raised by Hejhal and Rackner in their 1992 numerical
computations of Maass forms. We establish sharp upper and lower bounds for the
$L^2$-restrictions of these forms to certain curves on the modular surface.
These results, together with the Lindelof Hypothesis and known subconvex
$L^\infty$-bounds are applied to prove that locally the number of nodal domains
of such a form goes to infinity with its eigenvalue.
