PGL2 (Fℓ) number fields with rational companion forms

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Abstract

We give a list of PGL2(Fℓ) number fields for ℓ ≥ 11 which have rational companion forms. Our list has 53 fields and seems likely to be complete. Some of the fields on our list are very lightly ramified for their Galois group.

Original languageEnglish (US)
Pages (from-to)825-845
Number of pages21
JournalInternational Journal of Number Theory
Volume14
Issue number3
DOIs
StatePublished - Apr 1 2018

Bibliographical note

Funding Information:
The author's research was supported by grant #209472 from the Simons Foundation and grant DMS-1601350 from the National Science Foundation.

Publisher Copyright:
© 2018 World Scientific Publishing Company.

Keywords

  • Galois group
  • Number field
  • companion form
  • discriminant
  • modular form

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