Classical and overconvergent modular forms of higher level
Journal de théorie des nombres de Bordeaux, Volume 9 (1997) no. 2, pp. 395-403.

We define the notion overconvergent modular forms on Γ 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 Γ 1 (Np 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 (Np n )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 (Np 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.

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

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