Classical and overconvergent modular forms of higher level

Robert F. Coleman

Robert F. Coleman

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

Abstract (VO)
Résumé

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.

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.

EuDML MR Zbl

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

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

Bibliographie
Cité par

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