Hecke Operators and Γ(2) Subgroups Original Research Article

We introduce for each odd integer m an element θm of image[M2(image)]. We prove that these elements θm satisfy the usual algebraic relations between Hecke operators. The statement of the theorem is elementary but the proof uses essentially modular symbols and the theory of Hecke correspondences on modular curves defined by subgroups of Γ(2). We do not know any direct combinatorial proof of that theorem.