I'm given three matrices: M_1, M_2 and M_3, satisfying commutation relations (Einstein summation)

Eigenvalues of M_3 and their degeneracy is known and I need to find eigenvalues and degeneracies of M^2\equiv M_1^2+M_2^2+M_3^2.

I found that M^2 and M_3 commute, so they have common set of eigenvectors (but there are also degenerate vectors).

I don't really know how to start, so any tips are appreciated. Thanks in advance!