We consider a Banach algebra A, a nonzero element ϕ in ∆(A)∪ {0}, and a Banach A-bimodule X. We investigate ultrapowers denoted as (A)U and (ϕ), along with treating (X)U as a Banach (A)U -bimodule. We analyze H1((A)U ,(X)U ), with the constraint that (X)U ∈ SM(A)U(ϕ). Moreover, we establish a connection between H1((A)U , C) vanishing and H1((A)U ,(X)U ) vanishing. Subsequently, we relax the symmetry conditions of SM(A)U(ϕ)and explore character contractibility and character amenability of (A)U , which is referred to as ultracharacter contractibility and ultra-character amenability of A. In particular, we verify the ultra-character amenability for Lau products and group algebras.
