Can't install modules in a sub site --- Seeing Ajax error
Here is a list of items to check:


Clear all caches (it doesn't hurt, and occasionally helps solving various issues): if you get a WSOD while doing so, it indicates memory shortage.
Try running update.php (by typing an URL like http://www.yourdomain.com/update.php): if you get a Fatal error like "Allow memory size of ... bytes exhausted", it indicates memory shortage.
Verify if it is a memory shortage issue by increasing the memory a bit to check if there is any difference.

Assuming this is NOT a multi site, consider editing your /sites/default/settings.php, and change the line to set the memory limit. If it is a multi site, then edit the settings.php file related to the site where you are experiencing the problem.

That line in settings.php should look similar to this:

ini_set('memory_limit', '100M');

The '100M' in it might be some other number. Whatever the number is, try to increase it with like 50%, or maybe even double it to see what happens after you do so (of course do not forget to save the file after increasing that number).

If needed, refer to https://www.drupal.org/node/207036 for more details, eg if such 'ini_set' is not yet included in your settings.php file. As mentioned in that link: "Locate the PHP settings section and add that line at the end of that section".