  In this note, we consider discriminant forms that are given by the norm form
of real quadratic fields and their induced Weil representations. We prove that
there exists an isomorphism between the space of vector-valued modular forms
for the Weil representations that are invariant under the action of the
automorphism group and the space of scalar-valued modular forms that satisfy
some epsilon-condition, with which we translate Borcherds's theorem of
obstructions to scalar-valued modular forms. In the end, we consider an example
in the case of level 12.
