Classical and overconvergent modular forms of higher level

Coleman, Robert F.

Coleman, Robert F.

Journal de théorie des nombres de Bordeaux, Tome 9 (1997) no. 2, pp. 395-403.

Résumé
Abstract

Nous définissons la notion de forme modulaire surconvergente pour $Γ_{1} (N p^{n})$ où $p$ est un nombre premier, $N$ et $n$ sont des entiers et $N$ est premier à $p$ . Nous démontrons que toute forme primitive surconvergente pour $Γ_{1} (N p^{n})$ , de poids $k$ et dont la valeur propre de $U_{p}$ associée est de valuation strictement inférieure à $k - 1$ est une forme modulaire au sens classique.

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.

EuDML MR Zbl | 4 citations dans Numdam

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     author = {Coleman, Robert F.},
     title = {Classical and overconvergent modular forms of higher level},
     journal = {Journal de th\'eorie des nombres de Bordeaux},
     pages = {395--403},
     publisher = {Universit\'e Bordeaux I},
     volume = {9},
     number = {2},
     year = {1997},
     mrnumber = {1617406},
     zbl = {0942.11025},
     language = {en},
     url = {http://archive.numdam.org/item/JTNB_1997__9_2_395_0/}
}

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Coleman, Robert F. Classical and overconvergent modular forms of higher level. Journal de théorie des nombres de Bordeaux, Tome 9 (1997) no. 2, pp. 395-403. http://archive.numdam.org/item/JTNB_1997__9_2_395_0/

Bibliographie
Cité par

[1] Coleman R., Reciprocity Laws on Curves, Compositio 72 (1989), 205-235. | Numdam | MR | Zbl

[2] Coleman R., Classical and Overconvergent modular forms, Invent. Math. 124 (1996), 215-241. | MR | Zbl

[3] Edixhoven B., Stable models of modular curves and applications, Thesis, University of Utrecht (unpublished).

[4] Katz N., P-adic properties of modular schemes and modular forms Modular Functions of one Variable III, Springer Lecture Notes 350 (197), 69-190. | MR | Zbl

[5] Katz N. and B. Mazur, Arithmetic Moduli of Elliptic Curves, Annals of Math. Stud. 108, Princeton University Press, 1985. | MR | Zbl

[6] Mazur B. and A. Wiles, "Class fields and abelian extensions of Q", Invent. Math. 76 (1984), 179-330. | MR | Zbl

[7] Li W., "Newforms and functional equations, ", Math. Ann. 212 (1975), 285-315. | MR | Zbl

[8] Mazur B. and A. Wiles, "On p-adic analytic families of Galois representations", Compositio Math. 59 (1986), 231-264. | Numdam | MR | Zbl

[9] Ogg A., "On the eigenvalues of Hecke operators", Math. Ann. 179 (1969), 101-108. | MR | Zbl

[10] Coleman R., p-adic Banach spaces and families of modular forms, Invent. math. 127 (1992), 917-979. | MR | Zbl

[11] Coleman R., p-adic Shimura Isomorphism and p-adic Periods of modular forms, Contemp. Math. 165 (1997), 21-51. | MR | Zbl