  We prove multiplicative relations between certain Fourier coefficients of
degree 2 Siegel eigenforms. These relations are analogous to those for elliptic
eigenforms. We also provide two sets of formulas for the eigenvalues of degree
2 Siegel eigenforms. The first evaluates the eigenvalues in terms of the form's
Fourier coefficients, in the case $a(I) \neq 0$. The second expresses the
eigenvalues of index $p$ and $p^2$, for $p$ prime, solely in terms of $p$ and
$k$, the weight of the form, in the case $a(0)\neq 0$. From this latter case,
we give simple expressions for the eigenvalues associated to degree 2 Siegel
Eisenstein series.
