Journal of the Korean Mathematical Society (대한수학회지)

Korean Mathematical Society (대한수학회)
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EIGENVALUES AND CONGRUENCES FOR THE WEIGHT 3 PARAMODULAR NONLIFTS OF LEVELS 61, 73, AND 79

  • Cris Poor (Department of Mathematics Fordham University) ;
  • Jerry Shurman (Department of Mathematics Reed College) ;
  • David S. Yuen (Korean Mathematical Society)
  • Received : 2023.07.27
  • Accepted : 2024.04.19
  • Published : 2024.09.01
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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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References

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