Higher spin analogs of linearized topologically massive gravity and linearized new massive gravity

We suggest a new spin-4 self-dual model (parity singlet) and parity doublet in $D=2+1$. They are of higher order derivatives described by totally symmetric rank-4 tensor without extra auxiliary fields. Despite the they ghost free. find gauge invariant field combinations which allow us to show that canonical structure (spin-3) models follows same pattern its spin-2 (spin-1) counterpart after redefinitions. For $s=1,2,3,4$, spin-$s$ $2s-1$ $2s$ can be written terms three invariants. The cases $s=3$ $s=4$ restricted conformal spin symmetry as principle for defining linearized topologically massive gravity "New Massive Gravity" arbitrary integer spins. A key role our approach is played fact Cotton $D=2+1$ has only two independent components any spin.