  The explicit computation of the field of moduli of a closed Riemann surface
is, in general, a difficult task. In this paper, for each even integer $k \geq
2$, we consider a suitable $2$-real parameter family of non-hyperelliptic
pseudo-real Riemann surfaces of genus $g=1+(2k-3)k^{4}$. For each of them, we
compute its field of moduli and also a minimal field of definition.
