Equidistribution of Hecke eigenforms on the modular surface

For the orthonormal basis of Hecke eigenforms in $S_{2k}(\Gamma (1))$, one can associate with it a probability measure $d\mu _{k}$ on the modular surface $X = \Gamma (1) \backslash {\mathbf H}$. We establish that this new measure tends weakly to the invariant measure on $X$ as $k$ tends to infinity, and obtain a sharp estimate for the rate of convergence.