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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

Received: 8 October 2014

Accepted: 16 December 2014

Published: 29 May 2015


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.


Modular FormElliptic CurfDiophantine EquationGalois RepresentationMultiplicative Function