Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
8959482 | Journal of Number Theory | 2018 | 26 Pages |
Abstract
We prove congruences between cuspidal newforms and Eisenstein series of prime level, which generalize Ramanujan's congruence. Such congruences were recently found by Billerey and Menares, and we refine them by specifying the Atkin-Lehner eigenvalue of the newform involved. We show that similar refinements hold for the level raising congruences between cuspidal newforms of different levels, due to Ribet and Diamond. The proof relies on studying the new subspace and the Eisenstein subspace of the space of period polynomials for the congruence subgroup Î0(N), and on a version of Ihara's lemma.
Keywords
Related Topics
Physical Sciences and Engineering
Mathematics
Algebra and Number Theory
Authors
Radu Gaba, Alexandru A. Popa,