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You could try "Livin the Hida loca" and look at Theorem 2.1 of

H. Hida. On p-adic Hecke algebras for GL2 over totally real Felds. Ann. of Math. (2), 128(2):295–384, 1988.

I think this is a reference for your question.

You could try "Livin the Hida loca" and look at Theorem 2.1 of

H. Hida. On p-adic Hecke algebras for GL2 over totally real Felds. Ann. of Math. (2), 128(2):295–384, 1988.

You could try "Livin the Hida loca" and look at Theorem 2.1 of

H. Hida. On p-adic Hecke algebras for GL2 over totally real Felds. Ann. of Math. (2), 128(2):295–384, 1988.

I think this is a reference for your question.

Source Link

You could try "Livin the Hida loca" and look at Theorem 2.1 of

H. Hida. On p-adic Hecke algebras for GL2 over totally real Felds. Ann. of Math. (2), 128(2):295–384, 1988.