Two graded rings of Hermitian modular forms

Abstract

We give generators and relations for the graded rings of Hermitian modular forms of degree two over the rings of integers in $${\\mathbb {Q}}(\\sqrt{-7})$$\n \n Q\n (\n \n \n -\n 7\n \n \n )\n \n and $${\\mathbb {Q}}(\\sqrt{-11})$$\n \n Q\n (\n \n \n -\n 11\n \n \n )\n \n . 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.