Timeline for How to count to cusps of the modular curve $X_1(N)$, i.e., for the congruence subgroup $\Gamma_1(N)$
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| May 22, 2023 at 20:25 | comment | added | François Brunault | Dear @María, what point exactly in the computation is not clear? Something here or in Miyake? The only thing in my answer which is not in Miyake is the formula for the number of cusps as a product over the prime divisors of $N$. Does the confusion lie in going from Miyake's formula to that formula? Regarding 3., once you have understood Miyake, yes you will be able to enumerate the cusps. | |
| May 22, 2023 at 9:46 | comment | added | María | Thank you very much for your answer. I just have some doubts about it: 1. It is not so clear to me how the calculations works, I mean I don't understand how to get the number of the cusp for the case $X_1(\mathbb{C})$, could you please help me to understand this calculations. 2. I saw the reference and it is confusing to me how to deduce the formula. 3. We now know how to count the cusp, now I am wondering if there is some way to know which one are the cusp, explicitly? Do you know some way to do it? For example as we can do with $X(1)$: we know that the cusp is just one point, $\{\infty\}$. | |
| May 20, 2023 at 12:29 | history | answered | François Brunault | CC BY-SA 4.0 |