What are the political and social influences of Buddhism in Mauryan/Guptan India?

It was on account of the adoption of the Buddhist faith (dhamma) by Mauryan king Ashoka that Buddhism became the guiding principle of his political administration and policy. Through Ashoka's edicts, which were his means of communication in his empire, carved and chiselled on rocks and columns, social messages were also spread, calling for things like harmony between different faiths in society and respect for one another as social beings. Thus, politically Buddhism had the sanction of the state for the first time with the Mauryan empire. Embassies were sent propagating Buddha's message to other countries, most notably Sri Lanka.
The Guptas are not considered direct sponsors of Buddhism, yet being promoters of art and architecture, Buddhism saw a flouring of many different architectural style like the Mathura school of art. The Chinese scholar Fa-Hsein visited India during the Gupta period and noted that Buddhism was still a strong social presence, especially in eastern India. Samudragupta is also reputed to have had famous Buddhist scholars like Vasubandhu in his court.
Thus, Buddhism was a strong factor in the social and political landscape certainly with the Mauryans but also with the Guptas.
Source: Lamotte, E. History of Indian Buddhism (1988).

The Mauryan dynasty is most famous for the ruler Ashoka, who adopted Buddhism later in life, cultivating the religion’s spread throughout India. Ashoka was a patron of Buddhist artworks; throughout his empire, he erected pillars engraved with his political proclamations as well as Buddhist writings of compassion. These pillars suggest that Ashoka worked to spread his beliefs throughout the empire. In this way, religion and policy likely became intertwined among people living under Mauryan rule. Based on the pillars and their edicts, historians believe Ashoka to be a tolerant ruler, and they credit him with establishing Buddhism in India.
Though Gupta rulers were traditionally Hindu, some of them practiced Buddhism, a possible sign of their wanting to associate themselves with the splendor of the Maurya empire. In fact, artists in the Gupta period were the ones to create the canonical image of the Buddha with his monastic, clinging robe and softly sculpted body. That the government sponsored so many Buddhism-related artworks (which were, like Ashoka's pillars, located in accessible places) suggests that, as in the Mauryan dynasty, religion spread its influences into social and political life during the Gupta empire as well. Historians now view both dynasties as golden ages within Indian history, so perhaps the political embracing of Buddhism did bring temporary peace to the region.

Source: Kleiner, F. S. (2013). Gardner's art through the ages: A global history. Boston, MA: Wadsworth.