Are there any congruence subgroups other than $SL_2(\mathbb Z)$ which have exactly 1 cusp? By congruence subgroup, I mean a subgroup of $SL_2(\mathbb Z)$ containing $\Gamma(N)$ for some $N$.

This question was motivated by the comments on the answer to Generators of the graded ring of modular forms. In particular, if there are no such subgroups, then all congruence subgroups other than $SL_2(\mathbb Z)$ are generated in degree at most 5, with relations in degree at most 10, as follows from the comments on the answer to Generators of the graded ring of modular forms.

I have a feeling the answer to this question may be well known, but I could not find it in Diamond and Shurman or by a Google search.

Are there any congruence subgroups other than $\operatorname{SL}_2(\mathbb Z)$ which have exactly 1 cusp? By congruence subgroup, I mean a subgroup of $\operatorname{SL}_2(\mathbb Z)$ containing $\Gamma(N)$ for some $N$.

This question was motivated by the comments on the answer to Generators of the graded ring of modular forms. In particular, if there are no such subgroups, then all congruence subgroups other than $\operatorname{SL}_2(\mathbb Z)$ are generated in degree at most 5, with relations in degree at most 10, as follows from the comments on the answer to Generators of the graded ring of modular forms.

I have a feeling the answer to this question may be well known, but I could not find it in Diamond and Shurman or by a Google search.

Are there any congruence subgroups other than $SL_2(\mathbb Z)$ which have exactly 1 cusp? By congruence subgroup, I mean a subgroup of $SL_2(\mathbb Z)$ containing $\Gamma(N)$ for some $N$.

This question was motivated by the comments on the answer to Generators of the graded ring of modular forms. In particular, if there are no such subgroups, then all congruence subgroups other than $SL_2(\mathbb Z)$ are generated in degree at most 5, with relations in degree at most 10, as follows from the comments on the answer to Generators of the graded ring of modular forms.

I have a feeling the answer to this question may be well known, but I could not find it in Diamond and Shurman or by a Google search.

Are there any congruence subgroups other than $SL_2(\mathbb Z)$ which have exactly 1 cusp? By congruence subgroup, I mean a subgroup of $SL_2(\mathbb Z)$ containing $\Gamma(N)$ for some $N$.

This question was motivated by the comments on the answer to Generators of the graded ring of modular forms. In particular, if there are no such subgroups, then all congruence subgroups other than $SL_2(\mathbb Z)$ are generated in degree at most 5, with relations in degree at most 10, as follows from the comments on the answer to Generators of the graded ring of modular forms.

I have a feeling the answer to this question may be well known, but I could not find it in Diamond and Shurman or by a Google search.

Are there any congruence subgroups other than $SL_2(\mathbb Z)$ which have exactly 1 cusp? By congruence subgroup, I mean a subgroup of $SL_2(\mathbb Z)$ containing $\Gamma(N)$ for some $N$.

This question was motivated by the comments on the answer to Generators of the graded ring of modular forms. In particular, if there are no such subgroups, then I believe all congruence subgroups other than $SL_2(\mathbb Z)$ are generated in degree at most 5, with relations in degree at most 10.

I have a feeling the answer to this question may be well known, but I could not find it in Diamond and Shurman or by a Google search.

Are there any congruence subgroups other than $SL_2(\mathbb Z)$ which have exactly 1 cusp? By congruence subgroup, I mean a subgroup of $SL_2(\mathbb Z)$ containing $\Gamma(N)$ for some $N$.

This question was motivated by the comments on the answer to Generators of the graded ring of modular forms. In particular, if there are no such subgroups, then all congruence subgroups other than $SL_2(\mathbb Z)$ are generated in degree at most 5, with relations in degree at most 10, as follows from the comments on the answer to Generators of the graded ring of modular forms.

I have a feeling the answer to this question may be well known, but I could not find it in Diamond and Shurman or by a Google search.