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