In this talk, I will give a review of my recent joint works with Wentao Fan and Matilde Marcolli on a rationality phenomena and appearance of periods and motives in the heat kernel expansion of the Dirac-Laplacian of Bianchi IX gravity models with SU(2) symmetries. In the case of Bianchi IX gravitational instantons, which, in a succession of works by physicists and mathematicians, are characterized in terms of theta functions with characteristics, the terms in the expansion give rise to modular forms of weight 2, which we write explicitly in terms of Eisenstein series and the modular discriminant.