Longman Dictionary of Contemporary English - deeply

~ adv 1 a long way into something  (The parrot dug its claws deeply into my hand.) 2 deeply embarrassing/worrying/involved etc extremely or very much  (His remarks were deeply embarrassing.) 3 if you breathe deeply you completely fill your lungs with air 4 deeply held a deeply held belief or opinion is one that you are very sure about and feel very strongly about 5 deeply rooted a deeply rooted belief, opinion etc is difficult to change  (These traditions were deeply rooted in local custom.)