  We define a subspace of the space of holomorphic modular forms of weight
$k+1/2$ and level $4M$ where $M$ is odd and square-free. We show that this
subspace is isomorphic under the Shimura-Niwa correspondence to the space of
newforms of weight $2k$ and level $2M$ and that this is a Hecke isomorphism.
The space we define is a proper subspace of the orthogonal complement of the
Kohnen plus space if the Kohnen plus space is nonzero.
