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Slopes of the U7 operator acting on a space of overconvergent modular forms

Part of: Discontinuous groups and automorphic forms Arithmetic problems. Diophantine geometry

Published online by Cambridge University Press:  01 May 2012

L. J. P. Kilford  and
Ken McMurdy
L. J. P. Kilford
Affiliation:
School of Mathematics, University of Bristol, University Walk, Bristol, BS8 1TW, United Kingdom (email: l.kilford@gmail.com)
Ken McMurdy
Affiliation:
Department of Mathematics (TAS), Ramapo College of New Jersey, 505 Ramapo Valley Rd, Mahwah NJ 07430, USA (email: kmcmurdy@ramapo.edu)

Abstract

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Let χ be the primitive Dirichlet character of conductor 49 defined by χ(3)=ζ for ζ a primitive 42nd root of unity. We explicitly compute the slopes of the U7 operator acting on the space of overconvergent modular forms on X1(49) with weight k and character χ7k−6 or χ8−7k, depending on the embedding of ℚ(ζ) into ℂ7. By applying results of Coleman and of Cohen and Oesterlé, we are then able to deduce the slopes of U7 acting on all classical Hecke newforms of the same weight and character.

MSC classification

Secondary: 11F11: Holomorphic modular forms of integral weight 11F33: Congruences for modular and $p$-adic modular forms 14G35: Modular and Shimura varieties 14G22: Rigid analytic geometry
Type
Research Article
Information
LMS Journal of Computation and Mathematics , Volume 15 , May 2012 , pp. 113 - 139
Copyright
Copyright © London Mathematical Society 2012

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