  To understand the structure of hadrons it is important to know the PDF of
their constituents, the quarks and gluons. In our work we aim to compute the
first moment of the gluon PDF $\langle x \rangle_g$ for the nucleon. We follow
two possible approaches in order to extract the gluon moment: the
Feynman-Hellmann theorem and a direct method with smearing of the gluon
operator. We present preliminary results computed on $24^3 \times 48$ lattices
for the case where the Feynman-Hellman theorem is used and $32^3 \times 64$
lattices for the direct method, employing $N_f=2+1+1$ maximally twisted mass
fermions.
