  Let $K$ be a finite unramified extension of $\mathbb{Q}_p$, where $p>2$.
[CEGS22b] and [EG23] construct a moduli stack of two dimensional mod $p$
representations of the absolute Galois group of $K$. We show that most
irreducible components of this stack (including several non-generic components)
are isomorphic to quotients of smooth affine schemes. We also use this quotient
presentation to compute global sections on these components.
