Tagged Questions
3
votes
1answer
40 views
Formula for index of $\Gamma_1(n)$ in SL$_2(\mathbf Z)$
Is there a precise formula for the index of the congruence group $\Gamma_1(n)$ in SL$_2(\mathbf Z)$? I couldn't find it in Diamond and Shurman, and neither could I find an explicit formula with a ...
5
votes
1answer
159 views
A question about modular curves and base change
Let $X$ be a smooth projective geometrically connected curve over a number field $K$.
Suppose that the curve $X\times_{K,\sigma} \mathbf{C}$ is a modular curve for some $\sigma:K\to \mathbf{C}$.
Can ...
8
votes
1answer
81 views
Flatness of residual representations associated to modular forms
Let $f\in S_k(\Gamma_1(N),\chi)$ be a Hecke eigenform of weight $k\geq 2$, $p$ an odd prime not dividing $N$, and $K_f$ the number field generated by the Hecke eigenvalues of $f$. Fixing a prime ...
1
vote
1answer
118 views
Is there a fundamental domain for $\Gamma(2)$ contained in the following strip
Let $\Gamma(2)$ be the subgroup of $\mathrm{SL}_2(\mathbf{Z})$ satisfying the usual congruence conditions. It acts on the complex upper half-plane.
Does it have a fundamental domain contained in the ...
2
votes
0answers
45 views
What are the branch points of $X(n)\to X(1)$
Let $\Gamma \subset \mathrm{SL}_2(\mathbf{Z})$ be a finite index subgroup. Let $X_\Gamma \to X(1)$ be the corresponding morphism of compact connected Riemann surfaces (obtained by adding the cusps).
...
