“Wadjda” opens Friday at Sundance Cinemas. PG, 1:40, three stars out of four.

Wadjda wants a bike. She sees a beautiful bike strapped to the roof of a car, and it seems to be gliding in the air by her, just begging her to hop on board and ride. But bikes cost money. That is a problem for Wadjda, but not the biggest one.

The biggest one is that Wadjda is a 10-year-old girl in Saudi Arabia, where women are not allowed to drive cars or vote.

This simple premise is the basis for a landmark film. “Wadjda” is the first film to be made in Saudi Arabia, and it was made by first-time director Haifaa Al-Mansour on the sly. It is a fine film, engaging and heartfelt, and it will never be officially shown in Al-Mansour’s home country, where cinemas are banned.

Wadjda (Waad Mohammed) has her eye on a bike, but it costs 800 riyals, way more than she has. But she’s a plucky and resourceful kid in the manner of great child characters throughout cinema; the Chuck Taylor high-tops she wears under her black robe are a dead giveaway that this is no ordinary kid.

The stern headmistress at her school certainly senses Wadjda’s independent streak, and does her best to quash it. Wadjda hits upon a clever idea — there’s a Koran recitation contest at the school, with a grand prize of 1,000 riyals. She’ll study hard (even using  a Koran study video game) and win the prize. The irony of winning a Koran contest in order to buy something that the Koran prohibits is lost on her, but not on us

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Al-Mansour is a capable but not particularly distinguished filmmaker, and “Wadjda” has the sort of performances and cinematography you might expect out of a pretty good basic-cable drama. (Given that she’s now the only filmmaker in Saudi Arabia history, and a first-time one at that, one tends to be forgiving.) I did like the warm relationship between Wadjda and her mom (Reed Abdullah), who is nervous about her husband acquiring a second wife.

But the film really works because of Mohammed, who gives Wadjda a plucky charm and an indefatigable spirit, as well as the canniness to know when to hide both in the presence of stern adults like the headmistress. Her film is like she is, ostensibly playing by the rules, but throwing us enough sidewise glances to let us know that she’s much smarter than she appears.

“Wadjda” doesn’t despair at the chauvinistic culture it depicts; rather it shows us what a paper-thin facade it really is, behind which strong females like Wadjda and her mother are busily working for change, dignity — and maybe a cool new bike.