  We study complex hyperbolic disc bundles over closed orientable surfaces that
arise from discrete and faithful representations H_n->PU(2,1), where H_n is the
fundamental group of the orbifold S^2(2,...,2) and thus contains a surface
group as a subgroup of index 2 or 4. The results obtained provide the first
complex hyperbolic disc bundles M->{\Sigma} that: admit both real and complex
hyperbolic structures; satisfy the equality 2(\chi+e)=3\tau; satisfy the
inequality \chi/2<e; and induce discrete and faithful representations
\pi_1\Sigma->PU(2,1) with fractional Toledo invariant; where {\chi} is the
Euler characteristic of \Sigma, e denotes the Euler number of M, and {\tau}
stands for the Toledo invariant of M. To get a satisfactory explanation of the
equality 2(\chi+e)=3\tau, we conjecture that there exists a holomorphic section
in all our examples.
  In order to reduce the amount of calculations, we systematically explore
coordinate-free methods.
