Anomaly cancellation and modularity: E8*E8*E8 case

In [5] and [19], the authors gave anomaly cancellation formulas for the gauge groups E8,E8E8. In this paper, we mainly deal with the case of gauge group E8E8E8. Using the E8E8*E8 bundle, we construct some modular forms over SL2(Z). By these modular forms, we get some new anomaly cancellation formulas of characteristic forms.