Rings of Hilbert modular forms on totally real number fields with odd degree (Q1078231)

Let K be a totally real number field of odd degree \(n\geq 3\), \({\mathcal O}_ K\) be the ring of integers of K, \(\Gamma\) be \(PSL_ 2({\mathcal O}_ K)\) or a torsion-free subgroup of \(PSL_ 2({\mathcal O}_ K)\), M be the graded ring of Hilbert modular forms of even weight for \(\Gamma\). The author applies known results on the dimension of the space of modular forms of a given weight to the Hilbert series condition for a ring to be Gorenstein to prove that M is never a Gorenstein ring.