On the slopes of the U5 operator acting on overconvergent modular forms
L. J. P Kilford1
1 Department of Mathematics Royal Fort Annexe University of Bristol BS8 1TW, United Kingdom
Journal de théorie des nombres de Bordeaux, Tome 20 (2008) no. 1, pp. 165-182.

We show that the slopes of the U5 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:i∈ℕor14·8i+45:i∈ℕ,

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 Tp and U5 which is defined over Q5(54,3).

Nous démontrons que les pentes de l’opérateur U5 agissant sur 5-adique formes modulaires surconvergentes de poids k avec caractère de Dirichlet primitif χ de conducteur 25 sont

14·8i5:i∈ℕou14·8i+45:i∈ℕ.

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 Tp et U5 définie sur Q5(54,3).

DOI : 10.5802/jtnb.620

L. J. P Kilford 1

1 Department of Mathematics Royal Fort Annexe University of Bristol BS8 1TW, United Kingdom 
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L. J. P Kilford. On the slopes of the ${U_5}$ operator acting on overconvergent modular forms. Journal de théorie des nombres de Bordeaux, Tome 20 (2008) no. 1, pp. 165-182. doi : 10.5802/jtnb.620. https://jtnb.centre-mersenne.org/articles/10.5802/jtnb.620/

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