We define the notion overconvergent modular forms on where is a prime, and are positive integers and is prime to . We show that an overconvergent eigenform on of weight whose -eigenvalue has valuation strictly less than is classical.
Nous définissons la notion de forme modulaire surconvergente pour où est un nombre premier, et sont des entiers et est premier à . Nous démontrons que toute forme primitive surconvergente pour , de poids et dont la valeur propre de associée est de valuation strictement inférieure à est une forme modulaire au sens classique.
@article{JTNB_1997__9_2_395_0, 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://www.numdam.org/item/JTNB_1997__9_2_395_0/} }
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 SP - 395 EP - 403 VL - 9 IS - 2 PB - Université Bordeaux I UR - http://www.numdam.org/item/JTNB_1997__9_2_395_0/ LA - en ID - JTNB_1997__9_2_395_0 ER -
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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