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In this paper, a series of $\nu=2/5$ fractional quantum Hall wave functionsare constructed from conformal field theory(CFT). They share the sametopological properties with states constructed by Jain's composite fermionapproach. Upon exact lowest Landau level(LLL) projection, some of Jaincomposite fermion states would not survive if constraints on Landau levelindices given in the appendices of this paper were not satisfied. By contrast,states constructed from CFT always stay in LLL. These states are characterizedby different topological shifts and multibody relative angular momenta. As aby-product, in the appendices we prove the necessary conditions for general $\nu=p/(2p+1) $ composite fermion states to have nonvanishing LLL projection.

Construction of a series of new $\nu=2/5$ fractional quantum Hall wave functions by conformal field theory