I'm no expert but since they didn't ask for a cover letter, I would go with something short and to the point to summarize what's on your resume.
Dear _____,
Attached, please find a copy of my resume as my application for the position of________ as advertised through ________.
I am currently a ________ majoring in ________ and I am confident that I am well qualified for this position. I have experience in/with ______, ______, and _______ through my coursework and my employment at ________ as _________. Aside from my technical expertise, I am _______, ________, and ________.
I look forward to being able to meet with you and further discuss my qualifications.
Thank you for taking the time to review my application.
Sincerely,
________