  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 {\Gamma}^0(2) and
{\Gamma}_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 .
