p-adic families of Siegel modular cuspforms

P-adic Banach Spaces and Families of Modular Forms

Let p be a prime, Cp the completion of an algebraic closure of the p-adicnumbers Qp and K a finite extension of Qp contained in Cp. Let v be the valuation on Cp such that v(p) = 1 and let | | be the absolute value on Cp such that |x| = p for x ∈ Cp. Suppose N is a positive integer prime to p. Let X1(Np) denote the modular curve over K which represents elliptic curves with Γ1(Np)-structure and l...

SIEGEL MODULAR FORMS ( MOD p ) AND ALGEBRAIC MODULAR FORMS

In his letter [Ser96], J.-P. Serre proves that the systems of Hecke eigenvalues given by modular forms (mod p) are the same as the ones given by locally constant functions A×B/B × → F̄p, where B is the endomorphism algebra of a supersingular elliptic curve. After giving a detailed exposition of Serre’s result, we prove that the systems of Hecke eigenvalues given by Siegel modular forms (mod p) o...

Bounding slopes of p-adic modular forms

Let p be prime, N be a positive integer prime to p, and k be an integer. Let Pk(t) be the characteristic series for Atkin’s U operator as an endomorphism of p-adic overconvergent modular forms of tame level N and weight k. Motivated by conjectures of Gouvêa and Mazur, we strengthen a congruence in [W] between coefficients of Pk and Pk′ for k ′ p-adically close to k. For p − 1 | 12, N = 1, k = 0...

p-adic Banach modules of arithmetical modular forms and triple products of Coleman's families

For a prime number p ≥ 5, we consider three classical cusp eigenforms

Big image of Galois representations associated with finite slope p-adic families of modular forms