  We investigate, with the help of Monte-Carlo and exact-diagonalization
calculations in the spherical geometry, several compressible and incompressible
candidate wave functions for the recently observed quantum Hall state at the
filling factor $\nu=1/4$ in a wide quantum well. The quantum well is modeled as
a two-component system by retaining its two lowest subbands. We make a direct
connection with the phenomenological effective-bilayer model, which is commonly
used in the description of a wide quantum well, and we compare our findings
with the established results at $\nu=1/2$ in the lowest Landau level. At
$\nu=1/4$, the overlap calculations for the Halperin (5,5,3) and (7,7,1)
states, the generalized Haldane-Rezayi state and the Moore-Read Pfaffian,
suggest that the incompressible state is likely to be realized in the interplay
between the Halperin (5,5,3) state and the Moore-Read Pfaffian. Our numerics
shows the latter to be very susceptible to changes in the interaction
coefficients, thus indicating that the observed state is of multicomponent
nature.
