After you successfully register with immigration, you will receive your Irish Residence Permit (IRP).
Your IRP will detail the type of immigration permission you have.
There are different types of immigration permission. Each permission type has a stamp number. The stamp number indicates what type activities you can and cannot do in Ireland. You should understand the conditions of your immigration permissions/stamp number. Permission to study on a full time degree is indicated by Stamp 2.
You can learn more about IRP cards, immigration permissions and stamps on the Irish Immigration Services webpage.