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Explicit Action of Hecke Operators on Siegel Modular Forms

✍ Scribed by James Lee Hafner; Lynne H Walling

Publisher
Elsevier Science
Year
2002
Tongue
English
Weight
182 KB
Volume
93
Category
Article
ISSN
0022-314X

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✦ Synopsis

We develop an algorithm for determining an explicit set of coset representatives (indexed by lattices) for the action of the Hecke operators T(p), T j (p 2 ) on Siegel modular forms of fixed degree and weight. This algorithm associates each coset representative with a particular lattice W, pL Δ± W Δ± 1 p L where L is a fixed reference lattice. We then evaluate the action of the Hecke operators on Fourier series. Since this evaluation yields incomplete character sums for T j (p 2 ), we complete these sums by replacing this operator with a linear combination of T a (p 2 ), 0 [ a [ j. In all cases, this yields a clean and simple description of the action on Fourier coefficients.

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