Ms. Tolokonnikova was one of three members of the protest group who were convicted in 2012 for performing a protest concert in the Cathedral of Christ the Savior in Moscow. Ms. Tolokonnikova and her bandmate Maria Alyokhina served a year and nine months in prison before they were released under an amnesty law before the 2014 Winter Olympics in Sochi, Russia. Another member of the group, Yekaterina Samutsevich, had been released on parole.

In the video, Ms. Tolokonnikova plays, with a sly smile, Mr. Chaika, her old nemesis.

“I love Russia, I am a patriot, but I could live in Switzerland,” she sings.

The young women sway to the tinny rhythm, gorge on a lavish feast in a palatial setting and pout at the camera. One wears a bird mask, a reference to Mr. Chaika, whose name means “sea gull.” Ms. Tolokonnikova alternates between flapping her hands like wings and forming pistols with her fingers.

A framed portrait of President Vladimir V. Putin, the type that hangs in official offices here, looks down on Ms. Tolokonnikova as she eats a gold-painted loaf of bread. And there are subtle hints at life inside the zone, the Russian penal colony system, such as a checkerboard drawn on a table with spilled sugar. The game pieces are also lumps of sugar.

“Be humble, learn to obey, don’t worry about material stuff,” Ms. Tolokonnikova rhymes sarcastically.

“And son, if you do worry about material things in life, then be loyal to Putin forever, son,” Ms. Tolokonnikova raps softly. “You want to get away with murder, be loyal to your boss.”