Level-two scalar in covariant string quantization ($⟨S|S⟩=\frac{2}{25}(D-1)(26-D)$)

At $a=1$, let $k=\sqrt{2{\alpha }^{\prime }}p$, $k^2=-2$. The physical scalar $[{\alpha }_{-1}\cdot {\alpha }_{-1}+(D+4)(k\cdot {\alpha }_{-1}{)}^2/10+(D-1)k\cdot {\alpha }_{-2}/5]|p⟩$ has norm $2(D-1)(26-D)/25$. It is positive below 26, null at 26, and a string ghost state above 26. Matching the ordinary transverse spectrum removes this extra scalar at 26.