We give generators and relations for the graded rings of Hermitian modular forms of degree two over the rings of integers in $\mathbb{ Q}(\sqrt{ -7})$ and $\mathbb{ Q}(\sqrt{ -11})$. In both cases we prove that the subrings of symmetric modular forms are generated by Maass lifts. The computation uses a reduction process against Borcherds products which also leads to a dimension formula for the spaces of modular forms.
Categories: math.NT