Oh look a question, I can ramble a bit now!
No, just because you have a wizard school doesn't automatically mean you are writing Harry Potter. I'd say that your idea is still too vague to be called out as highly similar beyond superficial things, as the actual execution and writing style (along with plot focus and progression) will be what truly determines how similar it is to Harry Potter (if you ask me). Tone could also probably go in that list, but so could other things I imagine.
Granted, having a train ride to the wizard school is another superficial similarity, and one I question the intent behind, but it isn't inherently wrong or something that should be different. Do keep in mind that if your story does become a Harry Potter fan-fiction, I'd advise labeling it appropriately and being careful with canon character cameos.
Anyway, here are some questions:
- There is magic, but what is the setting? Modern adventure with a 'secret' magic world? Full blown fantasy? Weird sci-fi 'magic' post apocalypse facility?
- Is the protagonist a chosen one? Are they an orphan with an abusive home life?
- How dark does the story get? What maturity rating would it have / is it targeting the same audience as Harry Potter?
- How does the magic system work? Is it a soft or hard one, are there schools of magic or is it all just one broad thing? Is it super undefined or very rigorous?
- Are people split into four groups within the school based on personality dispositions?
I'll leave you with that, but keep in mind that you don't necessarily need to answer these questions, they may not matter at this stage or be irrelevant given your writing process, but as I understand it this is a coauthor story, so I will encourage communication between all the writers to ensure you have some sort of consistency between your parts, but more importantly, that you all agree with the direction the story writing process (and actual story) is heading in.
Thus, it should go without saying, if an author thinks it is too similar (and that this is bad) then you should probably look to differentiate your story more.
TL;DR
I'd say no, but there are other people who's opinions you should care about more in regards to this question. Anyway, best of luck with the story, coauthoring can be a challenge.