On the p-adic Eichler-Shimura isomorphism for ...-adic cusp forms.
We show that the slopes of the operator acting on 5-adic overconvergent modular forms of weight with primitive Dirichlet character of conductor 25 are given by eitherdepending on and .We also prove that the space of classical cusp forms of weight and character has a basis of eigenforms for the Hecke operators and which is defined over .
The purpose of this work is to carry out the first step in our four-step program towards the main conjecture for by the method of Eisenstein congruence on , where is an imaginary quadratic field. We construct a -adic family of ordinary Eisenstein series on the group of unitary similitudes with the optimal constant term which is basically the product of the Kubota-Leopodlt -adic -function and a -adic -function for . This construction also provides a different point of view of -adic...
We give a geometric definition of overconvergent modular forms of any -adic weight. As an application, we reprove Coleman’s theory of -adic families of modular forms and reconstruct the eigencurve of Coleman and Mazur without using the Eisenstein family.