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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 andwhen $p=2r_1r_2$ with $r_1$, $r_2$ two distinct odd primes. Some partialgeneralizations in higher genus are also presented.

Decomposition of some Witten-Reshetikhin-Turaev Representations into Irreducible Factors