Classical and overconvergent modular forms of higher level

Robert F. Coleman

Journal de théorie des nombres de Bordeaux (1997)

  • Volume: 9, Issue: 2, page 395-403
  • ISSN: 1246-7405

Abstract

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We define the notion overconvergent modular forms on Γ 1 ( N p n ) where p is a prime, N and n are positive integers and N is prime to p . We show that an overconvergent eigenform on Γ 1 ( N p n ) of weight k whose U p -eigenvalue has valuation strictly less than k - 1 is classical.

How to cite

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Coleman, Robert F.. "Classical and overconvergent modular forms of higher level." Journal de théorie des nombres de Bordeaux 9.2 (1997): 395-403. <http://eudml.org/doc/248007>.

@article{Coleman1997,
abstract = {We define the notion overconvergent modular forms on $\Gamma _1(Np^n)$ where $p$ is a prime, $N$ and $n$ are positive integers and $N$ is prime to $p$. We show that an overconvergent eigenform on $\Gamma _1(Np^n)$ of weight $k$ whose $U_p$-eigenvalue has valuation strictly less than $k - 1$ is classical.},
author = {Coleman, Robert F.},
journal = {Journal de théorie des nombres de Bordeaux},
keywords = {-adic overconvergent modular form},
language = {eng},
number = {2},
pages = {395-403},
publisher = {Université Bordeaux I},
title = {Classical and overconvergent modular forms of higher level},
url = {http://eudml.org/doc/248007},
volume = {9},
year = {1997},
}

TY - JOUR
AU - Coleman, Robert F.
TI - Classical and overconvergent modular forms of higher level
JO - Journal de théorie des nombres de Bordeaux
PY - 1997
PB - Université Bordeaux I
VL - 9
IS - 2
SP - 395
EP - 403
AB - We define the notion overconvergent modular forms on $\Gamma _1(Np^n)$ where $p$ is a prime, $N$ and $n$ are positive integers and $N$ is prime to $p$. We show that an overconvergent eigenform on $\Gamma _1(Np^n)$ of weight $k$ whose $U_p$-eigenvalue has valuation strictly less than $k - 1$ is classical.
LA - eng
KW - -adic overconvergent modular form
UR - http://eudml.org/doc/248007
ER -

References

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  1. [1] Coleman R., Reciprocity Laws on Curves, Compositio72 (1989), 205-235. Zbl0706.14013MR1030142
  2. [2] Coleman R., Classical and Overconvergent modular forms, Invent. Math.124 (1996), 215-241. Zbl0851.11030MR1369416
  3. [3] Edixhoven B., Stable models of modular curves and applications, Thesis, University of Utrecht (unpublished). 
  4. [4] Katz N., P-adic properties of modular schemes and modular forms Modular Functions of one Variable III, Springer Lecture Notes350 (197), 69-190. Zbl0271.10033MR447119
  5. [5] Katz N. and B. Mazur, Arithmetic Moduli of Elliptic Curves, Annals of Math. Stud.108, Princeton University Press, 1985. Zbl0576.14026MR772569
  6. [6] Mazur B. and A. Wiles, "Class fields and abelian extensions of Q", Invent. Math.76 (1984), 179-330. Zbl0545.12005MR742853
  7. [7] Li W., "Newforms and functional equations, ", Math. Ann.212 (1975), 285-315. Zbl0278.10026MR369263
  8. [8] Mazur B. and A. Wiles, "On p-adic analytic families of Galois representations", Compositio Math.59 (1986), 231-264. Zbl0654.12008MR860140
  9. [9] Ogg A., "On the eigenvalues of Hecke operators", Math. Ann.179 (1969), 101-108. Zbl0169.10102MR269597
  10. [10] Coleman R., p-adic Banach spaces and families of modular forms, Invent. math.127 (1992), 917-979. Zbl0918.11026MR1431135
  11. [11] Coleman R., p-adic Shimura Isomorphism and p-adic Periods of modular forms, Contemp. Math.165 (1997), 21-51. Zbl0838.11033MR1279600

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