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In this paper, we write down the local Brauer classes of the endomorphismalgebras of motives attached to non-CM primitive Hecke eigenforms for allsupercuspidal 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 unramifiedsupercuspidal 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 classesat non dihedral primes by using results similar to [MR2770587].  We provide some numerical examples using {Sage} and {LMFDB} supporting someof our theorems.

Supercuspidal ramifications and traces of adjoint lifts at good primes