The congruence subgroup
Γ
2
(
2
,
4
,
8
)
{\Gamma _2}(2,4,8)
of the group
Γ
2
{\Gamma _2}
of
4
×
4
4 \times 4
integral symplectic matrices is contained in
Γ
2
(
4
)
{\Gamma _2}(4)
and contains
Γ
2
(
8
)
{\Gamma _2}(8)
, with
Γ
2
(
n
)
{\Gamma _2}(n)
the principal congruence subgroup of level n. The Satake compactification of the quotient of the three-dimensional Siegel upper half space by
Γ
2
(
2
,
4
,
8
)
{\Gamma _2}(2,4,8)
is shown to be a complete intersection of ten quadrics in
P
13
{\mathbb {P}^{13}}
. We determine the space of global holomorphic three forms on this space, which coincides with the space of cusp forms of weight 3 on
Γ
2
(
2
,
4
,
8
)
{\Gamma _2}(2,4,8)
; it has dimension 2283. Finally, we study the action of the Hecke operators on this space and consider the Andrianov L-functions of some eigenforms.