On a congruence prime criterion for cusp forms on GL2 over number fields

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Let f be a normalized Hecke eigenform on GL2 over a number field F and let P be a prime ideal of a number field which contains the Galois closure of the number field which is generated by all Fourier coefficients of f over F . In this paper, we give a sufficient condition for P to be a congruence prime for f . This criterion is a generalization of congruence prime criteria which were known for the case of elliptic cusp forms by Hida, for the case where F is an imaginary quadratic field by Urban and for the case of Hilbert cusp forms by Ghate and Dimitrov to arbitrary number fields.

Original languageEnglish
Pages (from-to)149-207
Number of pages59
JournalJournal fur die Reine und Angewandte Mathematik
Issue number707
Publication statusPublished - Oct 1 2015
Externally publishedYes

All Science Journal Classification (ASJC) codes

  • Mathematics(all)
  • Applied Mathematics

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