  We study many-body ground states for the partial integer fillings of the
$N=1$ Landau level in graphene, by constructing a model that accounts for the
lattice scale corrections to the Coulomb interactions. Interestingly, in
contrast to the $N=0$ Landau level, this model contains not only pure delta
function interactions but also some of its derivatives. Due to this we find
several important differences with respect to the $N=0$ Landau level. For
example at quarter filling when only a single component is filled, there is a
degeneracy lifting of the quantum hall ferromagnets and ground states with
entangled spin and valley degrees of freedom can become favourable. Moreover at
half-filling of the $N=1$ Landau level, we have found a new phase that is
absent in the $N=0$ Landau level, that combines characteristics of the
Kekul\'{e} state and an antiferromagnet. We also find that according to the
parameters extracted in a recent experiment, at half-filling of the $N=1$
Landau level graphene is expected to be in a delicate competition between an AF
and a CDW state, but we also discuss why the models for these recent
experiments might be missing some important terms.
