In Iwaniec and Kowalski, the term nebentypus is mentioned several times in the book. Every time it seems to just refer to a character $\chi$. Since I don't see the authors defining nebentypus, can anyone give me a concise definition?
Thanks!
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A modular form is a nice function on the upper half plane that transforms nicely under congruence subgroups of $SL_2(\mathbb{Z})$. It is possible to twist it by a character $\chi$ by letting $\chi$ act on one of the matrix coefficient in the definition. In that case we call the modular form to have nebentype $\chi$. See the wikipedia page.
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$\begingroup$ Thank you for your answer. Just to make sure, so essentially it is a character but in this context we define it as nebentypus? $\endgroup$ Commented Apr 18, 2013 at 21:17
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$\begingroup$ @user73119, yes. $\endgroup$– user27126Commented Apr 18, 2013 at 21:17