Hecke operators on line bundles over modular curves

Given a principal congruence subgroup Γ=Γ(N)⊆SL2(Z), Connes and Moscovici have introduced a modular Hecke algebra A(Γ) that incorporates both the pointwise multiplicative structure of modular forms and the action of the classical Hecke operators. It is well known that a Γ-modular form g of weight k may be described as a global section of the k-th tensor power of a certain line bundle p(Γ):L(Γ)→Γ\H. The purpose of this paper is to develop a theory of modular Hecke algebras for Hecke correspondences between the line bundles L(Γ) that lift the classical Hecke correspondences between modular curves Γ\H.