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Linear subspace of polynomial ring

I am trying to compute a QQ-linear subspace W of a polynomial ring R over QQ. However, R does not seem to have a method like subspace. So what I would like to do is

R=PolynomialRing(QQ,'x',3)
x=R.gens()
W=R.subspace([x[0]^2,3*x[1]+x[0]])

For further purposes I still want to apply functions defined on the ring R to elements of W but also apply linear algebra methods (linear maps, eigenspaces, ...) to W.

I am sorry to bother you with this, it should be very easy, but I did not find a way to do it.