In this note we determine explicitly the dimension of Kohnen's spaces of half integral weight with odd square free level and arbitrary character $\chi$, and show that it coincides with that of spaces of modular cusp forms of weight $2k$ with square free level and character $\chi^2$.
"Remark on the dimension of Kohnen's spaces of half integral weight with square free level." Proc. Japan Acad. Ser. A Math. Sci. 78 (2) 18 - 21, Feb. 2002. https://doi.org/10.3792/pjaa.78.18