  We have performed a calculation of the $D\bar D$, $D\bar D^\ast$, $D^\ast\bar
D$, $D^\ast\bar D^\ast$ components in the wave function of the $\psi(3770)$.
For this we make use of the $^3P_0$ model to find the coupling of $\psi(3770)$
to these components, that with an elaborate angular momentum algebra can be
obtained with only one parameter. Then we use data for the $e^+e^-\to D\bar D$
reaction, from where we determine a form factor needed in the theoretical frame
work, as well as other parameters needed to evaluate the meson-meson selfenergy
of the $\psi(3770)$. Once this is done we determine the $Z$ probability to
still have a vector core and the probability to have the different meson
components. We find $Z$ about $80\sim85\%$, and the individual meson-meson
components are rather small, providing new empirical information to support the
largely $q\bar q$ component of vector mesons, and the $\psi(3770)$ in
particular.
