Several new two-variable elliptic genera

In this paper, we define several new two-variable elliptic genera for even dimensional spin manifolds which are the index for some Dirac operators and holomorphic $SL(2,Z)$, ${\mathrm{\Gamma }}_0(2)$, ${\mathrm{\Gamma }}^0(2)$, ${\mathrm{\Gamma }}_{\theta }$-Jacobi forms. By these Jacobi forms, we can get some $SL(2,\mathbf{Z})$ and ${\mathrm{\Gamma }}^0(2)$ modular forms. By these $SL(2,\mathbf{Z})$ and ${\mathrm{\Gamma }}^0(2)$ modular forms, we get some interesting anomaly cancellation formulas for spin manifolds.