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Let $\Gamma$ be a congruence groupsubgroup of $SL_2(\mathbb Z)$ and $\chi:\Gamma \to \mathbb{C}^*$ a character of $\Gamma$ with finite image. Is then $\ker(\chi)$ also a congruence group? If not, can someone give me a counterexample?
Let $\Gamma$ be a congruence group and $\chi:\Gamma \to \mathbb{C}^*$ a character of $\Gamma$. Is then $\ker(\chi)$ also a congruence group? If not, can someone give me a counterexample?
Let $\Gamma$ be a congruence subgroup of $SL_2(\mathbb Z)$ and $\chi:\Gamma \to \mathbb{C}^*$ a character of $\Gamma$ with finite image. Is then $\ker(\chi)$ also a congruence group? If not, can someone give me a counterexample?
Let $\Gamma$ be a congruence group and $\chi:\Gamma \to \mathbb{C}^*$ a character of $\Gamma$. Is then $\ker(\chi)$ also a congruence group? If not, can someone give me a counterexample?
