Let G be a split connected reductive group over a finite field Fp with algebraic closure k, fix an Iwahori subgroup B ⊂ G(Fp([[t]])) and let F l = G(k((t)))/Bk denote the affine flag variety of G. Let q denote a power of p and fix a prime l 6= p. In [GH], the authors study the Jordan-Hölder series for objects in the Hecke category P q (F l,Ql). This is the category of B-equivariant perverse Wei...