  We prove Ibukiyama's conjectures on Siegel modular forms of half-integral
weight and of degree 2 by using Arthur's multiplicity formula on the split odd
special orthogonal group $\SO_5$ and Gan-Ichino's multiplicity formula on the
metaplectic group $\Mp_4$. In the proof, the representation theory of the
Jacobi groups also plays an important role.

Number Theory;Representation Theory