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The command
S = [sum(a*b for (a,b) in zip(List, v)) for v in ListofVectors]
will return what you want, although it won't be printed how you want:
sage: S
[3-form on the 4-dimensional differentiable manifold U,
3-form on the 4-dimensional differentiable manifold U,
3-form on the 4-dimensional differentiable manifold U]
sage: S[0] == g + h
True
sage: S[1] == 2*g + h
True
