In this paper we study the PBW filtration on irreducible integrable highest weight representations of affine Kac-Moody algebras ĝ. The n-th space of this filtration is spanned by the vectors x1. xsv, where xi ∈ ĝ, s ≤ n, and v is a highest weight vector. For the vacuum module we give a conjectural description of the corresponding adjoint graded space in terms of generators and relations. For g of the type A1 we prove our conjecture and derive the fermionic formula for the graded character.