JavaScript (ES6), 5 characters
Thanks to @ETHproductions and @Taco for helping with this; this was a group project, and although the original idea was mine, many of the details are theirs.
[]+=`
It's fairly well established that any Javascript program can be written with the characters ([]()+...
also, we don't use v, at least not for the Turing-completeness proof
> So for example, we can do [[]+[]][+[]]["constructor"] to get at the constructor for a string, whose name is String, and then stringify it to get at the capital S character.