Eureka is a pale girl with striking turquoise hair and lavender eyes who pilots the Nirvash typeZERO. What sets her apart is how she relates to her mecha—she doesn't see it as a machine at all, but as a living being with its own consciousness and feelings. It's a pretty central part of who she is.
Socially, though, she struggles. She has a hard time connecting with other people and reading their emotions, which makes her come off as distant or awkward. She's known for appearing suddenly next to people without warning, which tends to startle them. Early on in the anime, she deals with frequent headaches that seem tied to Renton Thurston's presence, though this fades as the story goes on.
Despite her youth and emotional distance, Eureka is the adoptive mother to three kids: Maurice, Maeter, and Linck. She's genuinely uncertain about her role as a parent, though—she'll actually ask Renton for advice on how to discipline them or whether she's doing okay as a mom. It's one of the more human sides to her character.
A small note: her name isn't pronounced the way English speakers would naturally say it. It's "eau-wreck-uh" rather than "you-ree-ka." During the episode previews, she's just called "the girl" anyway.
Content compiled by AnimeList.moe from publicly available sources.