Abstract
Given a principal congruence subgroup Γ = Γ ( N ) ⊆ SL 2 ( 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 .
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