Null fields realizations of W3 from W(sl(4), sl(3)) and W(sl(3|1), sl(3)) algebras

We consider the nonlinear algebras W(sl(4), sl(3)) and W(sl(3|1), sl(3)) and find their realizations in terms of currents spanning conformal linearizing algebras. The specific structure of these algebras, allows us to construct realizations modulo null fields of the W3 algebra that lies in the cosets W(sl(4),sl(3))u(1) and W(sl(3|1),sl(3))u(1). Such realizations exist for the following values of the W3 algebra central charge: cW = −30, −407, −985, −2. The first two values are listed for the first time, whereas for the remaining values we get the new realizations in terms of an arbitrary stress tensor and u(1) × sl(2) affine currents.