  Let $K$ be a field of characteristic zero and $V$ a vector space of dimension
$m>1$ with a nondegenerate symmetric bilinear form $f:V\times V \rightarrow K$.
The Jordan algebra $B_m=K\oplus V$ of the form $f$ is a superalgebra with this
decomposition. We prove that the ideal of all the $2$-graded identities of
$B_m$ satisfies the Specht property and we compute the $2$-graded cocharacter
sequence of $B_m$.
