A construction of admissible image-modules of level image.

By using generalized vertex algebras associated to rational lattices, we construct explicitly the admissible modules for the affine Lie algebra image of level image. As an application, we show that the W(2,5) algebra with central charge c=-7 investigated in (J. Algebra 270 (2003) 115) is a subalgebra of the simple vertex operator algebra image.