  The Orlov spectrum and Rouquier dimension are invariants of a triangulated
category to measure how big the category is, and they have been studied
actively. In this paper, we investigate the singularity category
$\mathsf{D_{sg}}(R)$ of a hypersurface $R$ of countable representation type.
For a thick subcategory $\mathcal{T}$ of $\mathsf{D_{sg}}(R)$ and a full
subcategory $\mathcal{X}$ of $\mathcal{T}$, we calculate the Rouquier dimension
of $\mathcal{T}$ with respect to $\mathcal{X}$. Furthermore, we prove that the
level in $\mathsf{D_{sg}}(R)$ of the residue field of $R$ with respect to each
nonzero object is at most one.
