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GH from MO
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user42690
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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$$\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?

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?

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?

Source Link
user42690
user42690
  • 871
  • 4
  • 11

When is the image of a 2-dim l-adic representation associated to a modular form open

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?