Dear Forum,
I am not sure this is a designed feature or a bug....

If 'Base' is executed before 'Coefficients', then the (linearly
independent) generator used to define V becomes the (ordered) basis of V:

gap> V:=VectorSpace([Z(2)^0,Z(4)],GF(2));Base(V);Coefficients(V,Z(4));
VectorSpace( [ Z(2)^0, Z(2^2) ], GF(2) )
[ Z(2)^0, Z(2^2) ]
[ 0*Z(2), Z(2)^0 ]

However, if 'Coefficients' is executed before 'Base', then gap first
reversed the order of the generators of V to construct the (ordered)
basis of V:

gap> V:=VectorSpace([Z(2)^0,Z(4)],GF(2));Coefficients(V,Z(4));Base(V);
VectorSpace( [ Z(2)^0, Z(2^2) ], GF(2) )
[ Z(2)^0, 0*Z(2) ]
[ Z(2^2), Z(2)^0 ]

This rearrangement in the latter case is caused by the call 'Information(V)'

Akihiro Munemasa