How do you know it accepts JPEGs? Can you do something like
nerfarious_script.jpeg.exe
?
If you are authorized, try to upload several variants of files and proxy the application's response. Look for subtleties.
It may be suspectible to parameter tampering. In PHP, it would be something like
include $_REQUEST['filename’];
If it's not validating your upload parameter, try some fuzzing; for example, /../../ or command injection.