  Let $K$ be an imaginary quadratic number field of class number one and
$\mathcal{O}_K$ be its ring of integers. We show that, if the arithmetic
functions $f, g:\mathcal{O}_K\rightarrow \mathbb{C}$ both have level of
distribution $\vartheta$ for some $0<\vartheta\leq 1/2$ then the Dirichlet
convolution $f*g$ also have level of distribution $\vartheta$.
