On a congruence prime criterion for cusp forms on GL2 over number fields
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Kenichi Namikawa
Abstract
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.
This article contains a partially improved version of the author's thesis at Osaka University. The author would like to sincerely express his gratitude to his advisor, Professor Tadashi Ochiai, for valuable discussions during the preparation of this article.
The author is also grateful to Professor Haruzo Hida, Ming-Lun Hsieh and Tomonori Moriyama for valuable comments and suggestions. The author would like to thank the anonymous referees for careful reading of our paper and for his many useful suggestions.
© 2015 by De Gruyter
Articles in the same Issue
- Frontmatter
- Stable reduction of X0(p4)
- Flows of constant mean curvature tori in the 3-sphere: The equivariant case
- The Thurston norm and twisted Alexander polynomials
- Finite dimensional representations of Khovanov–Lauda–Rouquier algebras I: Finite type
- Continuity and finiteness of the radius of convergence of a p-adic differential equation via potential theory
- On a congruence prime criterion for cusp forms on GL2 over number fields
- A note on cancellation in totally definite quaternion algebras
- Warped product Einstein metrics on homogeneous spaces and homogeneous Ricci solitons
Articles in the same Issue
- Frontmatter
- Stable reduction of X0(p4)
- Flows of constant mean curvature tori in the 3-sphere: The equivariant case
- The Thurston norm and twisted Alexander polynomials
- Finite dimensional representations of Khovanov–Lauda–Rouquier algebras I: Finite type
- Continuity and finiteness of the radius of convergence of a p-adic differential equation via potential theory
- On a congruence prime criterion for cusp forms on GL2 over number fields
- A note on cancellation in totally definite quaternion algebras
- Warped product Einstein metrics on homogeneous spaces and homogeneous Ricci solitons
