Computations of vector-valued Siegel modular forms

2012/03/26 by Alexandru Ghitza, Ghitza, Alexandru, Nathan C. Ryan +2
Mathematics · #11F33 #11F46 #11F60 #11Y99 #Advanced Algebra and Geometry #Algebraic Geometry and Number Theory #Analytic Number Theory Research #FOS: Mathematics #Number Theory (math.NT)

paper · pdf · doi:10.48550/arxiv.1203.5611

openalex publication_date 2012/03/26 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We carry out some computations of vector valued Siegel modular forms of degree two, weight (k,2) and level one. Our approach is based on Satoh's description of the module of vector-valued Siegel modular forms of weight (k, 2) and an explicit description of the Hecke action on Fourier expansions. We highlight three experimental results: (1) we identify a rational eigenform in a three dimensional space of cusp forms, (2) we observe that non-cuspidal eigenforms of level one are not always rational and (3) we verify a number of cases of conjectures about congruences between classical modular forms and Siegel modular forms.

Related

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