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On the slopes of the  U 5 operator acting on overconvergent modular forms

L. J. P Kilford (2008)

Journal de Théorie des Nombres de Bordeaux

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 1 4 · 8 i 5 : i or 1 4 · 8 i + 4 5 : 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 ) .

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