On the slopes of the U 5 operator acting on overconvergent modular forms
Journal de théorie des nombres de Bordeaux, Volume 20 (2008) no. 1, p. 165-182

We show that the slopes of the U 5 operator acting on 5-adic overconvergent modular forms of weight k with primitive Dirichlet character χ of conductor 25 are given by either

14·8i5:ior14·8i+45:i,

depending on k and χ.

We also prove that the space of classical cusp forms of weight k and character χ has a basis of eigenforms for the Hecke operators T p and U 5 which is defined over Q 5 (5 4,3).

Nous démontrons que les pentes de l’opérateur U 5 agissant sur 5-adique formes modulaires surconvergentes de poids k avec caractère de Dirichlet primitif χ de conducteur 25 sont

14·8i5:iou14·8i+45:i.

Nous prouvons aussi que l’espace de forms parabolique de poids k et caractère χ a une base des formes propres pour les opérateurs de Hecke T p et U 5 définie sur Q 5 (5 4,3).

@article{JTNB_2008__20_1_165_0,
     author = {Kilford, L. J. P},
     title = {On the slopes of the~${U\_5}$ operator acting on overconvergent modular forms},
     journal = {Journal de th\'eorie des nombres de Bordeaux},
     publisher = {Universit\'e Bordeaux 1},
     volume = {20},
     number = {1},
     year = {2008},
     pages = {165-182},
     doi = {10.5802/jtnb.620},
     zbl = {1211.11059},
     mrnumber = {2434162},
     zbl = {pre05543195},
     language = {en},
     url = {http://www.numdam.org/item/JTNB_2008__20_1_165_0}
}
Kilford, L. J. P. On the slopes of the ${U_5}$ operator acting on overconvergent modular forms. Journal de théorie des nombres de Bordeaux, Volume 20 (2008) no. 1, pp. 165-182. doi : 10.5802/jtnb.620. http://www.numdam.org/item/JTNB_2008__20_1_165_0/

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