The graded ring of Hermitian modular forms of degree 2 over [formula omitted

Abstract

We describe the graded ring of symmetric Hermitian modular forms of even weights and degree 2 over Q ( −2 ) in terms of generators and relations. All the 8 generators of weight up to 12 are Maaß lifts and some of them can also be obtained from Borcherds products. Moreover, we construct generators for the module over this ring consisting of all Hermitian modular forms with respect to the commutator subgroup. As an application the field of Hermitian modular functions over Q ( −2 ) is determined. Finally, we construct 5 algebraically independent symmetric Hermitian modular forms in terms of theta series.