  In this paper, we write down the local Brauer classes of the endomorphism
algebras of motives attached to non-CM primitive Hecke eigenforms for all
supercuspidal primes in terms of traces of adjoint lifts at auxiliary primes.
  We give an alternative proof of the result for odd primes $p$ obtained in
[MR3391026] and write down the ramification formulas for odd unramified
supercuspidal primes of level zero also removing a mild hypothesis of
[MR3391026].
  We also give a complete description of ramifications for $p=2$.
  The philosophy of adjoint lifts help us to determine the local Brauer classes
at non dihedral primes by using results similar to [MR2770587].
  We provide some numerical examples using {Sage} and {LMFDB} supporting some
of our theorems.
