The Belle Collaboration has measured the complete set of angular coefficient functions for the decays ${\bar B} \to D^*\,(D\,\pi)\,\ell\,{\bar \nu}_{\ell}$, where $\ell = e,\,\mu$, in four bins of the variable $w={m_B^2+m_{D^*}^2-q^2 \over 2\, m_B\, m_{D^*}}$, with $q$ the momentum of the lepton pair. In SM this measurement is instrumental in determining the hadronic form factors in the $B \to D^*$ matrix elements of the SM weak current, thereby refining the measurement of $\lvert V_{cb} \lvert$. On the other hand, it can be used to assess the impact of possible new physics contributions. I consider an extension of the SM effective Hamiltonian that governs this mode, incorporating the complete set of Lorentz invariant $d = 6$ operators compatible with the gauge symmetry of the theory. The measured angular coefficient functions play a pivotal role in constraining the couplings in the generalized effective Hamiltonian.