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It seems you are looking for the terse printing mode:
sage: K = Qp(2, print_mode='terse')
sage: R.<x> = K[]
sage: L.<w> = K.extension(x^3 + 4*x^2 + 2)
sage: w^3
2097150 + 2097148*w^2 + O(w^63)
There's a section PRINTING in the reference manual which has more details.
