Classical and overconvergent modular forms of higher level

@article{Coleman1997ClassicalAO,
  title={Classical and overconvergent modular forms of higher level},
  author={Robert F. Coleman},
  journal={Journal de Theorie des Nombres de Bordeaux},
  year={1997},
  volume={9},
  pages={395-403}
}
  • R. Coleman
  • Published 1997
  • Mathematics
  • Journal de Theorie des Nombres de Bordeaux
We define the notion overconvergent modular forms on 03931 (Npn) where p is a prime, N and n are positive integers and N is prime to p. We show that an overconvergent eigenform on 03931 (Npn) of weight k whose Upeigenvalue has valuation strictly less than k 1 is classical. In this note we define a notion of overconvergent modular form of level where lV is a positive integer, p is a prime, (N, p) = 1 1 and generalize the main result of [2]. That is, we show that overconvergent forms of level… 

Slopes of overconvergent modular forms

In the first part of this thesis, we consider the slopes of the U2 operator acting on spaces of 2-adic overconvergent modular forms with nontrivial weight-character of tame level 1. We establish a

p-Adic family of half-integral weight modular forms via overconvergent Shintani lifting

The classical Shintani map (Shintani, Nagoya Math J 58:83–126, 1975) is the Hecke-equivariant map from the space of cusp forms of integral weight to the space of cusp forms of half-integral weight.

p-adic modular forms of non-integral weight over Shimura curves

This work defines an analogue of the sheaves of kth invariant differentials over the Shimura curves the authors are interested in, for any p-adic character, to introduce the notion of overconvergent modular form of anyp-adic weight.

Slopes of eigencurves over boundary disks

Let p be a prime number. We study the slopes of $$U_p$$Up-eigenvalues on the subspace of modular forms that can be transferred to a definite quaternion algebra. We give a sharp lower bound of the

Lubin–Tate theory and overconvergent Hilbert modular forms of low weight

  • Gal Porat
  • Mathematics
    Israel Journal of Mathematics
  • 2022
Let K be a finite extension of ℚ p and let Γ be the Galois group of the cyclotomic extension of K . Fontaine’s theory gives a classification of p -adic representations of Ga ( $$\overline K /K$$ K ¯

Density of classical points in eigenvarieties

In this short note, we study the geometry of the eigenvariety parametrising p-adic automorphic forms for GL(1) over a number field K, as constructed by Buzzard. We show that if K is not totally real

On a p-adic extension of the Jacquet-Langlands correspondence to weight 1

AbstractIn this paper, we consider a novel version of the classical Jacquet-Langlands correspondence, explore a p-adic extension of the correspon-dence, and as an explicit example we find an

N T ] 2 0 N ov 2 00 3 Slopes of overconvergent 2-adic modular forms

Let p be a prime, and let N be a positive integer coprime to p. Let Mk(Γ1(N);Qp) denote the weight k modular forms of level Γ1(N) defined over Qp. In recent years, work of Coleman and others (for

QUATERNIONIC MODULAR FORMS OF ANY WEIGHT

In this work we give a geometric definition, as sections of line bundles, of p-adic analytic families of overconvergent modular forms attached to an indefinite quaternion algebra over ℚ. As a

References

SHOWING 1-9 OF 9 REFERENCES

Classical and overconvergent modular forms

The purpose of this article is to use rigid analysis to clarify the relation between classical modular forms and Katz’s overconvergent forms. In particular, we prove a conjecture of F. Gouvea [G,

Arithmetic moduli of elliptic curves

This work is a comprehensive treatment of recent developments in the study of elliptic curves and their moduli spaces. The arithmetic study of the moduli spaces began with Jacobi's "Fundamenta Nova"

Class fields of abelian extensions of Q

Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 179 0. Notation and preliminaries . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

On $p$-adic analytic families of Galois representations

© Foundation Compositio Mathematica, 1986, tous droits réservés. L’accès aux archives de la revue « Compositio Mathematica » (http: //http://www.compositio.nl/) implique l’accord avec les conditions

Reciprocity laws on curves

© Foundation Compositio Mathematica, 1989, tous droits réservés. L’accès aux archives de la revue « Compositio Mathematica » (http: //http://www.compositio.nl/) implique l’accord avec les conditions

P-adic Banach spaces and families of modular forms

Let p be a prime, Cp the completion of an algebraic closure of the p-adic numbers Qp and K a nite extension of Qp contained in Cp. Let v be the valuation on Cp such that v(p) = 1 and let | | be the

p-adic Shimura Isomorphism and p-adic Periods of modular forms

  • Contemp. Math
  • 1997