  We classify the trace anomaly for parity-invariant non-relativistic
Schr\"odinger theories in 2+1 dimensions coupled to background Newton-Cartan
gravity. The general anomaly structure looks very different from the one in the
z=2 Lifshitz theories. The type A content of the anomaly is remarkably
identical to that of the relativistic 3+1 dimensional case, suggesting the
conjecture that an a-theorem should exist also in the Newton-Cartan context.
  Erratum: due to an overcounting of the number of linearly-independent terms
in the basis, the type A anomaly disappears if Frobenius condition is imposed.
See appended erratum for details. This crucial mistake was pointed out to us in
arXiv:1601.06795.
