  Let L be the even unimodular lattice of signature (2,10), In the paper [FS]
we considered the subgroup O(L)^+ of index two in the orthogonal group. It acts
biholomorphically on a ten dimensional tube domain H_{10}. We found a 715
dimensional space of modular forms with respect to the principal congruence
subgroup of level two O^+(L)[2]. It defines an everywhere regular birational
embedding of the related modular variety into the 714 dimensional projective
space. In this paper, we prove that this space of orthogonal modular forms is
related to a space of theta series. The main tool is a modular embedding of
H_{10} into the Siegel half space of degree 16. As a consequence the modular
forms in the 715 dimensional space can be obtained as restrictions of the
simplest among all theta series.
