Abstract
The Shimura correspondence is a fundamental tool in the study of half-integral weight modular forms. In this paper, we prove a Shimura-type correspondence for spaces of half-integral weight cusp forms which transform with a power of the Dedekind eta multiplier twisted by a Dirichlet character. We prove that the lift of a cusp form of weight λ+1/2 and level N has weight 2λ and level 6N, and is new at the primes 2 and 3 with specified Atkin-Lehner eigenvalues. This precise information leads to arithmetic applications. For a wide family of spaces of half-integral weight modular forms we prove the existence of infinitely many primes ℓ which give rise to quadratic congruences modulo arbitrary powers of ℓ.
Original language | English (US) |
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Article number | 109655 |
Journal | Advances in Mathematics |
Volume | 447 |
DOIs | |
State | Published - Jun 2024 |
Keywords
- Congruences for modular forms
- Eta multiplier
- Shimura lift
ASJC Scopus subject areas
- General Mathematics