  We decompose into irreducible factors the ${\rm SU}(2)$
Witten-Reshetikhin-Turaev representations of the mapping class group of a genus
$2$ surface when the level is $p=4r$ and $p=2r^2$ with $r$ an odd prime and
when $p=2r_1r_2$ with $r_1$, $r_2$ two distinct odd primes. Some partial
generalizations in higher genus are also presented.
