  We study the algebras of hermitian automorphic forms for the lattice
$L_n=diag(1,1,\ldots,1,-1)$ and for the field $K=\mathbb{Q}(\sqrt{-d})$ such
that $p=2$ is unramified and the ring of integers $\mathcal{O}_K$ is a p.i.d.
We prove that for $d>7$ these algebras can't be free. When $d=7$ and $d=3$ we
give an estimate for the dimension of the symmetric spaces for which these
algebras might be free. We also compare our results with the known results for
$d=3$.
