  New effective $\Lambda N$ interactions are proposed for the density dependent
relativistic mean field model. The multidimensionally constrained relativistic
mean field model is used to calculate ground state properties of eleven known
$\Lambda$ hypernuclei with $A\ge 12$ and the corresponding core nuclei. Based
on effective $NN$ interactions DD-ME2 and PKDD, the ratios $R_\sigma$ and
$R_\omega$ of scalar and vector coupling constants between $\Lambda N$ and $NN$
interactions are determined by fitting calculated $\Lambda$ separation energies
to experimental values. We propose six new effective interactions for $\Lambda$
hypernuclei: DD-ME2-Y1, DD-ME2-Y2, DD-ME2-Y3, PKDD-Y1, PKDD-Y2 and PKDD-Y3 with
three ways of grouping and including these eleven hypernuclei in the fitting.
It is found that the two ratios $R_\sigma$ and $R_\omega$ are correlated well
and there holds a good linear relation between them. The statistical errors of
the ratio parameters in these effective interactions are analyzed. These new
effective interactions are used to study the equation of state of hypernuclear
matter and neutron star properties with hyperons.
