We define Hilbert-Siegel modular forms and Hecke "operators" acting on them.As with Hilbert modular forms, these linear transformations are not linearoperators until we consider a direct product of spaces of modular forms (withvarying groups), modulo natural identifications we can make between certainspaces. With Hilbert-Siegel forms we identify several families of naturalidentifications between certain spaces of modular forms. We associate theFourier coefficients of a form in our product space to even integral lattices,independent of a basis and choice of coefficient rings. We then determine theaction of the Hecke operators on these Fourier coefficients, paralleling theresult of Hafner and Walling for Siegel modular forms (where the number fieldis the field of rationals).
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