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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 ) .

One special class of modular forms and group representations

Galina V. Voskresenskaya (1999)

Journal de théorie des nombres de Bordeaux

In this article we consider one special class of modular forms which are products of Dedekind η -functions and the relationships between these functions and representations of finite groups.

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