The distribution of the eigenvalues of Hecke operators
  For each prime $p$, we determine the distribution of the $p^{th}$ Fourier coefficients of the Hecke eigenforms of large weight for the full modular group. As $p\to\infty$, this distribution tends to the Sato--Tate distribution. 
J. Brian Conrey, William Duke, David W. Farmer