  In this paper, the effects of adding spatial conformal symmetry to the
asymptotic symmetry group of an asymptotically conformally flat spacetime are
studied. It is shown that, in addition to the BMS group, only the dilations of
the spatial conformal generators keep the corresponding boundary conditions
conformally invariant under hypersurface deformations. We prove that in order
to attain (i) a well-defined symplectic structure and (ii) a finite and (iii)
integrable conserved charge, these conditions are satisfied simultaneously when
admitting Regge-Teitelboim and twisted Henneaux-Troessaert parity conditions,
where the latter also contain supertranslation invariance. The conserved
dilation charge contains nonzero terms independent of the field variables,
giving a nonvanishing effect on the boundary. The dilation symmetry also
modifies the ADM mass, which is another physical effect of the conformal
symmetry.
