Patrick Schwarzenegger doesn’t think his famous father has much to do with his plum role on the third season of The White Lotus.

“I know there are people who’ll say I only got this role because of who my dad is,” Schwarzenegger said of his dad, The Terminator star and former California governor Arnold Schwarzenegger, in an interview for the latest edition of The Sunday Times. “They’re not seeing that I’ve had 10 years of acting classes…worked on my characters for hours on end or the hundreds of rejected auditions I’ve been on.”

He plays Saxon Ratliff, whose family is staying at the resort on the Max anthology series, which premiered this month. The son of Timothy (Jason Isaacs) and Victoria (Par­ker Posey), Saxon works for his father when they’re not in Thailand.

“Of course, it’s frustrating,” Schwarzenegger told the publication, “and you can get boxed in, and you think at that moment, ‘I wish I didn’t have my last name.’ But that’s a small moment. I would never trade my life with anyone. I’m very fortunate to have the life and family that I have, the parents I have, and the lessons and values they’ve instilled in me.”

Schwarzenegger is the third child of the Kindergarten Cop star and journalist Maria Shriver, a niece of late U.S. President John F. Kennedy. He began acting well before he was even in high school, earning some of his first credits in David Spade comedy The Benchwarmers, Adam Sandler comedy Grown Ups 2, and on an episode of TV’s Scream Queens, which was co-created by Ryan Murphy. Cut to last year, when he played the high-profile part of former NFL standout Tim Tebow in the season of American Sports Story TV series that focused on Aaron Hernandez.

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Earlier this month, Schwarzenegger told Jimmy Kimmel on Jimmy Kimmel Live!, that his family had watched the first two seasons of the Max show together. It aired the same night that they all regularly gather for dinner anyway.

He said it had been “a dream of mine” to be on the series. That went for Shriver, too.

“Every time we would watch the episodes,” he said, “my mom would be like, ‘Why aren’t you on the show?’ And my sister’s like, ‘You need to fire your agents. Why are you not on this show?’ And I was just, like, ‘Hopefully, one day.’ And then I got the audition for the third season, and…I didn’t tell them.”

Thousands of other actors were auditioning, too, so he didn’t know if he would actually be cast.

“And then I got the call back with Raechal Shewfelt Mike White, and I was like, I’m not gonna tell them for that. And then I booked it,” Schwarzenegger said, adding that he was prohibited from telling anyone. He only told his fiancée, but then, on a family trip, his mom and sister suspected the couple were keeping a secret and that it must be that she was pregnant. So he broke the good news, and there were tears all around.

“There was just this domino effect of us all crying…at a restaurant,” Schwarzenegger said.

The White Lotus airs Sundays at 9 p.m. ET on HBO.