In this talk, we introduce the notion of the generalized principal subspaces, which generalizes the Feigin-Stoyanovsky type principal subspaces. Certain Fermionic (combinatorial) bases and character formula of the Generalized principal subspaces are given. As an application, we descibe the branching rule of the intermediate vertex subalgebra \(V=V_{E_{7+1/2}}\), and show the modular invariance of the correlation function of \(V\).