  We present results on the lower moments of the nucleon generalized parton
distri butions within lattice QCD using two dynamical flavors of degenerate
twisted mass fermions. Our simulations are performed on lattices with three
different values of the lattice spacings, namely $a=0.089$ fm, $a=0.070$ fm and
$a=0.056$ fm, allowing the investigation of cut-off effects. The volume
dependence is examined using simulations on two lattices of spatial length
$L=2.1$ fm and $L=2.8$ fm. The simulations span pion masses in the range of
260-470 MeV. Our results are renormalized non-perturbatively and the values are
given in the $\bar{\rm MS}$ scheme at a scale $ \mu=2$ GeV. They are chirally
extrapolated to the physical point in order to compare with experiment. The
consequences of these results on the spin carried by the quarks in the nucleon
are investigated.
