A note on modular properties of non-principal and non-coprincipal admissible $C_2^{(1)}$-modules of integer level

For the affine Lie algebra $C_2^{(1)}$ we study non-principal and non-coprincipal admissible modules of integer level and their quantum Hamiltonian reduction, and show that they have ${\mathrm{\Gamma }}_0(2)$-modular invariance.