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} }
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…
49 Citations
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N T ] 2 0 N ov 2 00 3 Slopes of overconvergent 2-adic modular forms
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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…
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References
SHOWING 1-9 OF 9 REFERENCES
Classical and overconvergent modular forms
- Mathematics
- 1995
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
- Mathematics
- 1985
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
- Mathematics
- 1984
Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 179 0. Notation and preliminaries . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .…
On $p$-adic analytic families of Galois representations
- Mathematics
- 1986
© 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
- Mathematics
- 1989
© 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
- Mathematics
- 1997
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