What is the decomposition of of 120 and 128 reps of $SO(16)$ under $SO(12)\times SO(4)$?

Question

$E_8\supset SO(16)$

$248=120+128$

What is the decomposition of of 120 and 128 reps of $SO(16)$ under $SO(12)\times SO(4)$?

Answer 1

$SO(4)\sim SU(2)\times SU(2)$

$SO(16)\supset SO(12) \times SU(2)\times SU(2) $

$120=(3,1,1)+(1,3,1)+(2,2,12)+(1,1,66)$

$128=(2,1,32)+(1,2,\bar{32})$