Equidistribution of Hecke Eigenforms on the Arithmetic Surface Γ0(N)\H Original Research Article

Given the orthonormal basis of Hecke eigenforms in S2k(Γ(1)), Luo established an associated probability measure dμk on the modular surface Γ(1)\H that tends weakly to the invariant measure on Γ(1)\H. We generalize his result to the arithmetic surface Γ0(N)\H where Ngreater-or-equal, slanted1 is square-free