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This is one way:

sage: LL = L.change_ring(S.quo(u3))
sage: LL
Laurent Series Ring in z over Quotient of Multivariate Polynomial Ring in u1, u2, u3 over Rational Field by the ideal (u3)
sage: LL(f)
-4*z - 4/5*u1bar*z^5 + (-4/9*u1bar^2 - 8/9*u2bar)*z^9 + (-4/13*u1bar^3 - 24/13*u1bar*u2bar)*z^13 + (-4/17*u1bar^4 - 48/17*u1bar^2*u2bar - 24/17*u2bar^2 + 16/17*u1bar + 16/17*u2bar + 16/17)*z^17 + O(z^20)