Open Access

Modular forms with large coefficient fields via congruences

  • Luis Víctor Dieulefait1Email author,
  • Jorge Jiménez Urroz2 and
  • Kenneth Alan Ribet3
Research in Number Theory20151:2

DOI: 10.1007/s40993-015-0003-9

Received: 8 October 2014

Accepted: 16 December 2014

Published: 29 May 2015

Abstract

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.