  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.
