# 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…
• Mathematics
• 2002
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
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.
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.
• Mathematics
• 2014
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
• 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 ¯
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
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
• Mathematics
• 2008
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
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

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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