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Korean Mathematical Society JKMS

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J. Korean Math. Soc. 2024; 61(5): 997-1033

Online first article August 26, 2024      Printed September 1, 2024

https://doi.org/10.4134/JKMS.j230390

Copyright © The Korean Mathematical Society.

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

Cris Poor , Jerry Shurman , David S. Yuen

Fordham University; Reed College; 92-1507 Punawainui St.

Abstract

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We use Borcherds products to give a new construction of the weight~$3$
paramodular nonlift eigenform~$f_N$ for levels~$N=61,73,79$.
We classify the congruences of~$f_N$ 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.

Keywords: Paramodular cusp form, Hecke eigenvalues, congruence

MSC numbers: Primary 11F46; Secondary 11F30, 11F50

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