  Let $r \in \BC$ be a complex number, and $d \in \BZ_{\ge 2}$ a positive
integer greater than or equal to 2. Ashihara and Miyamoto introduced a vertex
operator algebra $\Vam$ of central charge $dr$, whose Griess algebra is
isomorphic to the simple Jordan algebra of symmetric matrices of size $d$. In
this paper, we prove that the vertex operator algebra $\Vam$ is simple if and
only if $r$ is not an integer.
  Further, in the case that $r$ is an integer (i.e., $\Vam$ is not simple), we
give a generator system of the maximal proper ideal $I_{r}$ of the VOA $\Vam$
explicitly.
