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  • Research Article
  • Open Access

Modular forms with large coefficient fields via congruences

  • 1Email author,
  • 2 and
  • 3
Research in Number Theory20151:2

https://doi.org/10.1007/s40993-015-0003-9

  • Received: 8 October 2014
  • Accepted: 16 December 2014
  • Published:

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.

Keywords

  • Modular Form
  • Elliptic Curf
  • Diophantine Equation
  • Galois Representation
  • Multiplicative Function

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