Level lowering for GU(1,2)

Mazur’s principle gives a criterion under which an irreducible mod $\mathrm{\ell }$ Galois representation arising from a modular form of level $Np$ (with $p$ prime to $N$) can also arise from a modular form of level $N\mathrm{.}$ We prove an analogous result showing that a mod $\mathrm{\ell }$ Galois representation arising from a stable cuspidal automorphic representation of the unitary similitude group $G=\mathrm{G}\mathrm{U}(1,2)$ which is Steinberg at an inert prime $p$ can also arise from an automorphic representation of $G$ that is unramified at $p$.