On the Trace of the Representation of SL(2,Z/NZ) in the Space of Modular Forms of Half Integral Weight

We determine explicitly the trace of the representation of SL(2,Z ⁄NZ ) in the space of modular forms of half integral weight and derive an explicit formula of the multiplicities of all irreducible components occuring in the representation of SL(2,Z ⁄pZ ) in the space of modular forms of half integral weight, which yields an analogue of Eichler’s results in the case of modular forms of half integral weight.