I've been a hiring manager and an HR Supervisor. I currently assist the HR Manager at my place of work.
I, personally, would follow up with a phone call to confirm that your e-mail was received and convey your continued interest in the position.
We accept applications, by appointment only, every single week. It can get pretty overwhelming. Some people are very persistant too early because we let everyone know that if we are considering them, we need time to check their references. That, in itself, can be a matter of phone tag. The next step in the process, after the references check out, is for them to come back and meet with the other department managers that they will also be working directly with. Then there is discussion and submission of a background check. Whether or not an applicant can be hired also depends on that. Then there is a 4-hour orientation.
I'm just mentioning this because the hiring process CAN take some time, even if the online situation may be different from the interpersonal requirements of many positions.
You've sent an e-mail. I would follow up tomorrow with a phone call as Fridays can be crazy busy.
Don't get discouraged. Remember that the people you submitted your information to probably have a million other things that they juggle behind the scenes. That's always been true in my case.
Definitely follow up and call. See if you can get a feel for where things stand. Remind them, personally, of your interest, and let the "process" happen.
Best wishes!
Did you get an idea of how many other people they were considering?