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.
I think this is a reference for your question.