Solution
= Solution
Applying the <Clebsch-Gordan decomposition for SU2> gives
$$
\boxed{V_4\otimes V_3\cong V_7\oplus V_5\oplus V_3\oplus V_1},
$$
and
$$
V_3\otimes V_3\cong V_6\oplus V_4\oplus V_2\oplus V_0.
$$
On the summand $V_{6-2j}$, interchange of the two tensor factors acts by $(-1)^j$; this is the <flip parity in the SU2 tensor square>. The even-$j$ summands make the <symmetric square>, so
$$
\boxed{S^2V_3\cong V_6\oplus V_2}.
$$