Determination of Siegel eigenforms
by Michael Volpato
Abstract: In the early 20th century, Hecke and Mordell proved that an eigenform for the action of the Hecke algebra on the space of modular forms, is completely determined by its first Fourier coefficient and its Hecke eigenvalues. We generalize this to higher dimensions to show that a Siegel eigenform is completely determined by those Fourier coefficients indexed by maximal quadratic lattices and its Hecke eigenvalues. We will assume no prior knowledge of the theory of modular forms.