Daws's cotype conjecture for coefficient spaces

Let $\Gamma$ be a discrete group, let $1\leq p\leq 2$, and let $q$ be its conjugate exponent, so that

$$\frac{1}{p}+\frac{1}{q}=1.$$

Let $B_p(\Gamma)$ denote the coefficient space associated with isometric representations on $q$-spaces. Daws's cotype conjecture. The Banach space $B_p(\Gamma)$ has cotype $q$. This conjecture would supply the cotype step needed to deduce $T_1(\Gamma)\subseteq\ell^q(\Gamma)$ from the preceding coefficient-space inclusion. It is attributed in the paper to Daws and is presented as an unresolved conjecture.