Is $Y(4008)$ possibly a $1^{--}$ $\psi (3^3{S}_1)$ state?

The strong decays of the radially excited $\psi (3^3{S}_1)$ state are studied within the ${}^3{P}_0$ model. As a believed $\psi (3^3{S}_1)$, some strong decay widths and relevant ratios of $\psi (4040)$ are calculated in the model. The theoretical results are consistent with experiments. In a similar way, as a possible $\psi (3^3{S}_1)$, the same strong decay widths and relevant ratios of $Y(4008)$ are presented. Our study indicates that $Y(4008)$ is hard to be identified with a $\psi (3^3{S}_1)$ charmonium once it is confirmed under the $D^{\ast }{\bar{D}}^{\ast }$ threshold, but it is very possibly a $\psi (3^3{S}_1)$ charmonium once it is confirmed above the $D^{\ast }{\bar{D}}^{\ast }$ threshold by experiment.