Modular forms with large coefficient fields via congruences

We use the theory of congruences between modular forms to prove the existence of newforms with square-free level having a fixed number of prime factors such that the degree of their coefficient fields is arbitrarily large. We also prove a similar result for certain almost square-free levels.

Bibliographic Details
Authors: Dieulefait, Luis, Jiménez Urroz, Jorge|||0000-0002-2395-4478, Ribet, Keneth
Format: article
Publication Date:2015
Country:España
Institution:Universitat Politècnica de Catalunya (UPC)
Repository:UPCommons. Portal del coneixement obert de la UPC
Language:English
OAI Identifier:oai:upcommons.upc.edu:2117/81139
Online Access:https://hdl.handle.net/2117/81139
https://dx.doi.org/10.1007/s40993-015-0003-9
Access Level:Open access
Keyword:Numerical analysis
Anàlisi numèrica
Classificació AMS::65 Numerical analysis::65L Ordinary differential equations
Àrees temàtiques de la UPC::Matemàtiques i estadística::Anàlisi numèrica::Mètodes numèrics
Description
Summary:We use the theory of congruences between modular forms to prove the existence of newforms with square-free level having a fixed number of prime factors such that the degree of their coefficient fields is arbitrarily large. We also prove a similar result for certain almost square-free levels.