 First massive GSO-projected Neveu–Schwarz states

At NS level $3/2$, the light-cone families are $b_{-3/2}^i|0⟩$, ${\alpha }_{-1}^i{b}_{-1/2}^j|0⟩$, and three distinct $b_{-1/2}$ oscillators. Their dimensions are $8+64+\left(\genfrac{}{}{0ex}{}{8}{3}\right)=128$. All have odd fermion-excitation parity. They assemble into the massive Spin group representations $44+84$, a symmetric traceless tensor and a three-form of Spin(9).