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

L. J. P Kilford[1]

  • [1] Department of Mathematics Royal Fort Annexe University of Bristol BS8 1TW, United Kingdom

Journal de Théorie des Nombres de Bordeaux (2008)

  • Volume: 20, Issue: 1, page 165-182
  • ISSN: 1246-7405

Abstract

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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 ∈ ℕ or 1 4 · 8 i + 4 5 : 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  T p and  U 5 which is defined over  Q 5 ( 5 4 , 3 ) .

How to cite

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Kilford, L. J. P. "On the slopes of the ${U_5}$ operator acting on overconvergent modular forms." Journal de Théorie des Nombres de Bordeaux 20.1 (2008): 165-182. <http://eudml.org/doc/10826>.

@article{Kilford2008,
abstract = {We show that the slopes of the $U_5$ operator acting on 5-adic overconvergent modular forms of weight $k$ with primitive Dirichlet character $\chi $ of conductor 25 are given by either\[ \left\lbrace \frac\{1\}\{4\}\cdot \left\lfloor \frac\{8i\}\{5\}\right\rfloor : i \in \mathbb\{N\}\right\rbrace \text\{ or \}\left\lbrace \frac\{1\}\{4\}\cdot \left\lfloor \frac\{8i+4\}\{5\}\right\rfloor : i \in \mathbb\{N\}\right\rbrace , \]depending on $k$ and $\chi $.We also prove that the space of classical cusp forms of weight $k$ and character $\chi $ has a basis of eigenforms for the Hecke operators $T_p$ and $U_5$ which is defined over $\mathbf\{Q\}_5(\@root 4 \of \{5\},\sqrt\{3\})$.},
affiliation = {Department of Mathematics Royal Fort Annexe University of Bristol BS8 1TW, United Kingdom},
author = {Kilford, L. J. P},
journal = {Journal de Théorie des Nombres de Bordeaux},
keywords = {overconvergent modular forms; slopes of Hecke operators; modular curves},
language = {eng},
number = {1},
pages = {165-182},
publisher = {Université Bordeaux 1},
title = {On the slopes of the $\{U_5\}$ operator acting on overconvergent modular forms},
url = {http://eudml.org/doc/10826},
volume = {20},
year = {2008},
}

TY - JOUR
AU - Kilford, L. J. P
TI - On the slopes of the ${U_5}$ operator acting on overconvergent modular forms
JO - Journal de Théorie des Nombres de Bordeaux
PY - 2008
PB - Université Bordeaux 1
VL - 20
IS - 1
SP - 165
EP - 182
AB - We show that the slopes of the $U_5$ operator acting on 5-adic overconvergent modular forms of weight $k$ with primitive Dirichlet character $\chi $ of conductor 25 are given by either\[ \left\lbrace \frac{1}{4}\cdot \left\lfloor \frac{8i}{5}\right\rfloor : i \in \mathbb{N}\right\rbrace \text{ or }\left\lbrace \frac{1}{4}\cdot \left\lfloor \frac{8i+4}{5}\right\rfloor : i \in \mathbb{N}\right\rbrace , \]depending on $k$ and $\chi $.We also prove that the space of classical cusp forms of weight $k$ and character $\chi $ has a basis of eigenforms for the Hecke operators $T_p$ and $U_5$ which is defined over $\mathbf{Q}_5(\@root 4 \of {5},\sqrt{3})$.
LA - eng
KW - overconvergent modular forms; slopes of Hecke operators; modular curves
UR - http://eudml.org/doc/10826
ER -

References

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