SL(2,Z) modular forms and Witten genus in odd dimensions

By some SL(2, Z) modular forms introduced in [4] and [10], we construct some modular forms over SL2(Z) and some modular forms over Γ^0(2) and Γ_0(2) in odd dimensions. In parallel, we obtain some new cancellation formulas for odd dimensional spin manifolds and odd dimensional spin^c manifolds respectively. As corollaries, we get some divisibility results of index of the Toeplitz operators on spin manifolds and spin^c manifolds .