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* The weight  is typically a positive integer.<br/>
* For odd , only the zero function can satisfy the second condition.<br/>
* The third condition is also phrased by saying that  is "holomorphic at the cusp", a terminology that is explained below. Explicitly, the condition means that there exist some  such that , meaning  is bounded above some horizontal line.<br/>
* The second condition for <br/>
:: <br/>
:reads<br/>
::<br/>
:respectively. Since  and  <a href="page.php?w=generating_set_of_a_group">generate</a> the group , the second condition</p><p>
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