Vertex algebraic structure of principal subspaces of basic A2n(2)-modules

We obtain a presentation of the principal subspace of the basic A2n(2)-module, n≥1n≥1. We show that its full character is given by the Nahm sum of the tadpole Dynkin diagram Tn=A2n/Z2Tn=A2n/Z2. This character is conjecturally modular after certain specializations. We prove the modularity property in the case of the affine Lie algebra of type A4(2).