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You forgot to pass map=True to get the maps.

K.<a> = CyclotomicField(11)
Q = K.primes_above(3)[0]
KQ = K.residue_field(Q)
VQ, fr, to = KQ.vector_space(map=True)

Then:

sage: to(a)
(0, 1, 0, 0, 0)

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