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Eigenvalues and congruences for the weight 3 paramodular nonlifts of levels 61, 73, and 79

2023/02/01 by Cris Poor, Poor, Cris, Jerry Shurman +3
Mathematics · #11F46 #Advanced Algebra and Geometry #Algebraic Geometry and Number Theory #Algebraic structures and combinatorial models #FOS: Mathematics #Number Theory (math.NT)

paper · pdf · doi:10.48550/arxiv.2302.00764

openalex publication_date 2023/02/01 · openalex created_date 2023/02/04 · openalex updated_date 2026/07/28

Abstract

We use Borcherds products to give a new construction of the weight 3 paramodular nonlift eigenform fN for levels N = 61, 73, 79. We classify the congruences of fN to Gritsenko lifts. We provide techniques that compute eigenvalues to support future modularity applications. Our method does not compute Hecke eigenvalues from Fourier coefficients but instead uses elliptic modular forms, specifically the restrictions of Gritsenko lifts and their images under the slash operator to modular curves.

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