# Definition of nebentypus in $L$-functions.

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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Thank you for your answer. Just to make sure, so essentially it is a character but in this context we define it as nebentypus? –  user73119 Apr 18 '13 at 21:17
@user73119, yes. –  user27126 Apr 18 '13 at 21:17