It was unfortunate that you were caught while there were so many others like you. You should honestly present the same thing (as you have written here) to authorities and sincerely apologize for your behaviour. You should also assure them for not repeating same thing in future. Tell them your parent’s position on disclosing this fact to them and convey them how ashamed you feel. Finally say sorry, sorry, sorry…..and mean it too. Any sensible person will forgive you If you have good reputation otherwise.