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