# Tagged Questions

Let $\Gamma_0(m)$ be the subgroup of $SL(2,\mathbb{Z})$ which is defined as follows: $$\Gamma_0(m)=\left\{ \left( \begin{array}{cc} a & b \\ c & d \end{array} \right) \in SL(2, \mathbb{Z} : c ... 1answer 46 views ### Proving addition and multiplication (1)Show that addition and multiplication mod n are associative operations. (2)Show that there are both an additive and a multiplicative identity. (3)Show that multiplication distributes over ... 2answers 159 views ### Order of special linear group SL_2 (F) [duplicate] In ex. 1.2.3 on p.21 of Diamond's A first course in modular forms, I was trying to show that$$|SL_2(\mathbb{Z}/N \mathbb{Z})|=N^3 \prod_{p|N}(1-1/p^2).$$First of all, I knew that If F is a field ... 1answer 140 views ### In one version of the Modularity Theorem, what does “arise from modular forms” mean? One version of Modularity Theorem says that The elliptic curves with rational j-values arise from modular forms. Where$$j(\tau)=1728\frac{g_2^3(\tau)}{\Delta(\tau)}$$I know every ... 1answer 77 views ### Why the kernel of isogeny is finite? It is said that the kernel of a isogeny is finite because it is discrete and complex tori are compact. I have some questions about this. 1. Following is my reason for the kernel is discrete. ... 1answer 236 views ### Question about weight 2 Eisenstein series I'm new to modular form, reading the book A First Course in Modular Forms We have the weight 2 Eisenstein series$$ G_2(\tau)=\sum_{c\in\mathbb{Z}}\sum_{d\in\mathbb{Z}_c'}\frac{1}{(c\tau+d)^2}  ...
Let $\Gamma$ be a congruence subgroup, $s$ be a cusp of $\Gamma$, $\sigma \in SL_{2}(\mathbb{Z})$ be the map which sends $\infty$ to $s$, and $\Gamma_{s} = \{\gamma \in \Gamma \mid \gamma(s) = s\}$. ...