The paper can be found here:


<http://link.springer.com/content/pdf/10.1007%2FBF01078890.pdf>


EDIT: Russian original available at [LINK](http://www.mathnet.ru/php/archive.phtml?wshow=paper&jrnid=faa&paperid=2422&option_lang=eng) 


In his proof of assertion 1, he "reduces to the case where $x = i\infty$. He says that for any $g\in M$ and $\gamma\in\text{SL}\_2(\mathbb{Z})$, there is some $h\in\Gamma(N)$ such that $g\gamma(i\infty) = \gamma h(i\infty)$.


How does he get that?


Also, this he says in his proof of assertion 2 that via the Petersson inner product, $\|\omega\| = \|\omega|\_g\|$ for all $g\in M$ implies that $\omega|\_g = \omega$ for all $g\in M$. He claims this follows from the triangle inequality.


I don't see why $\|\omega\| = \|\omega|\_g\|$ (since $g$ has determinant $p$, isn't $\|\omega|\_g\| = p^2\|\omega\|$?)


I also don't see why this implies that $\omega|\_g = \omega$.


I've been stuck on this for a while.


Any help would be much appreciated.


Thanks,


* will



quick question about Drinfeld's 2-page paper "Two Theorems on Modular Curves"
This is Theorem 2.3, page 64 in Lang's book "Introduction to Modular forms". 


