A seventh born girl born from a seventh child of a magic family is expected to have great powers but they do not manifest. Eventually she's sent to a school for people without magic and learns she can weave through a computer. She and her friend work to save the world from a dangerous nothing that consumes magic. Before or after this she's taken to another world to be coached on how to work her powers by an old man who calls her Catori (sometimes).
2 Answers
The Worldweavers series by Alma Alexander?
From the description of the first book, Gift of the Unmage:
Thus says Cheveyo: mage, teacher, the first person in Thea's life to remain unimpressed by her lineage as Double Seventh, the seventh child of two seventh children. From birth, great things were expected of Thea, gradually replaced by puzzled disappointment as it became evident her magical abilities are, at most, minimal. Now, with Cheveyo, Thea has begun to weave herself a new magical identity, infused with elements of the original worlds where Cheveyo and others like him walk. But back home, she attends the Academy, the one school on earth for those who, like her, can't do magic.
One of the Goodreads reviews mentions computer magic.
There's a book that seems to be a fairly close match, Gift of the Unmage (2007) by Alma Alexander.
Quoting from the blurb on Goodreads:
Thus says Cheveyo: mage, teacher, the first person in Thea's life to remain unimpressed by her lineage as Double Seventh, the seventh child of two seventh children. From birth, great things were expected of Thea, gradually replaced by puzzled disappointment as it became evident her magical abilities are, at most, minimal. Now, with Cheveyo, Thea has begun to weave herself a new magical identity, infused with elements of the original worlds where Cheveyo and others like him walk. But back home, she attends the Academy, the one school on earth for those who, like her, can't do magic. It is at the Academy that Thea realizes she will indeed have to fight, since her enemies are hungrier and more dangerous than she thought. What's more, her greatest strength may be the very powerlessness she has resisted for so long.
One of the reviews mentions that Thea can use computers to do magic:
All in all, the Native American elements were interesting, but an awkward blend with the later scenes in Thea's school and the computer magic. Her ability to access other worlds through computers seemed sort of contrived and random--I guess since in her world, she and computers were both supposed to be unmagical, that somehow allowed her to use them to access her otherworldly powers?