  We show that for every finitely presented pro-$p$
nilpotent-by-abelian-by-finite group $G$ there is an upper bound on
$\dim_{\mathbb{Q}_p} (H_1(M, \mathbb{Z}_p) \otimes_{\mathbb{Z}_p} \mathbb{Q}_p
)$, as $M$ runs through all pro-$p$ subgroups of finite index in $G$.
