An alternative (the next July 31st on a Tuesday, in 1984) should be given some consideration, however. Interestingly, this chart works pretty well, too. Here the sun in Leo is in trine to Uranus and square to Scorpio, suggesting the same themes of Light versus Dark, access to magic and higher mind, and a destiny to lead. And, remarkably, in the spring before this 11th birthday (1993), transiting Saturn is opposite Harry's moon, a very similar aspect to the one that occurred for the 1979/90 chart! In passing, I'll note that many of the gods and heroes of antiquity (for example, Venus) are "twice-born," and thus have two birth charts.
So, do we have Harry Potter's true horoscope? And is Harry Potter real? That's for you to decide.