  Motivated by the recent discovery of a canyon of conductance suppression in a
two-level equal spin quantum dot system [Phys. Rev. Lett. $\bf{104}$, 186804
(2010)] the transport through this system is studied in detail. At low bias and
low temperature a strong current suppression is found around the electron-hole
symmetry point independent of the couplings, in agreement with previous
results. By means of a Schrieffer-Wolff transformation we are able to give an
intuitive explanation to this suppression in the low-energy regime. In the
general situation, numerical simulations are carried out using quantum rate
equations. The simulations allow for the prediction of how the suppression is
affected by the couplings, the charging energy, the position of the energy
levels, the applied bias, and the temperature. We find that away from
electron-hole symmetry, the parity of the couplings is essential for the
current suppression. It is also shown how broadening, interference, and a
finite interaction energy cause a shift of the current minimum away from
degeneracy. Finally we see how an increased population of the upper level leads
to current peaks on each side of the suppression line. At sufficiently high
bias we discover a coherence-induced population inversion.
