What do you mean by a banner? No advertising banners are allowed on free hosted WordPress.com blogs. What is the URL of the blog in question wearing the Academica theme please?
Do you mean a custom image header? See here for details on how the theme is designed http://theme.wordpress.com/themes/academica/ scroll down to Quick specs:
The suggested header image dimensions are 960 by 300 (width, height). However, the height is flexible so you can upload a smaller cropped image if you wish.
Featured images in the sticky posts slider are also 960 by 300, but are fixed in height and width.
All other featured images are 120 width, and 80 in height. These images are displayed on posts on the home page, on archive pages, and on the search results page.