Hecke eigenvalues and relations for degree 2 Siegel Eisenstein series

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6 Citations (Scopus)

Abstract

We evaluate the action of Hecke operators on Siegel Eisenstein series of degree 2, square-free level N and arbitrary character, without using knowledge of their Fourier coefficients. From this we construct a basis of simultaneous eigenforms for the full Hecke algebra, and we compute their eigenvalues. As well, we obtain Hecke relations amond the Eisenstein series. Using these Hecke relations in the case that the character is trivial, we generate a basis for the space of Eisenstein series from one of the Eisenstein series.
Translated title of the contributionHecke eigenvalues and relations for degree 2 Siegel Eisenstein series of square-free level
Original languageEnglish
Number of pages24
JournalJournal of Number Theory
Volume132
Issue number11
DOIs
Publication statusPublished - Nov 2012

Keywords

  • Siegel modular form
  • Eisenstein series
  • Hecke operators

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