In Buddhist cosmology, what heaven is ruled by the god Śakra?

In Buddhist cosmology, Trāyastriṃśa is the heaven ruled by the god Śakra.

Trāyastriṃśa, whose name means “the Heaven of the Thirty-Three,” is one of the deva realms in Buddhist cosmology. It is traditionally located on or above Mount Sumeru, the cosmic mountain at the center of many Buddhist world systems.

Śakra, also known as Sakka in Pali sources and identified with Indra in some Indian traditions, presides over this heaven. Buddhist texts portray him as a powerful but still impermanent deity rather than an eternal creator god.

Trāyastriṃśa is part of samsara, the cycle of birth and death. Beings born there enjoy long lives and great pleasures, but they eventually die and may be reborn elsewhere. This distinguishes it from nirvana, which is liberation from samsara rather than a heavenly location.