Hybrid subconvexity bounds for twists of $\mathrm{G}{\mathrm{L}}_2\times \mathrm{G}{\mathrm{L}}_2$ $L$-functions

In this paper, we prove hybrid subconvexity bounds for $\mathrm{G}{\mathrm{L}}_2\times \mathrm{G}{\mathrm{L}}_2$ Rankin–Selberg $L$-functions twisted by a primitive Dirichlet character $\chi$ modulo a prime power, in the $t$ and depth aspects.