I know the following theorems by Serre:

1, The 2-dim l-adic representation associated to a non-CM elliptic curve is open.

2, The 2-dim l-adic representation associated the weight-12 cusp form $\delta$ has open image (even before Deligne's construction of 2-dim l-adic representations).

So is there any general theorem about When the image of a 2-dim l-adic representation associated to a modular form is open?