I'd like to ask the following question:



> 
> Are the **Brauer character values** of $kG$-modules (where $k$ and $G$ are finite) in MAGMA computed with respect to the standard $p$-modular system described in the book of Lux and Pahlings\* (chapter 4 in Representations of Groups: A computational Approach)?
> 
> 
> 


Remark 1: I am asking this, because I would like to inflate Brauer characters from factor groups and then induce them to a common supergroup and I'd like to get consistent results.


Remark 2: I posted this question on math.stackexchange.com (see <https://math.stackexchange.com/questions/3239642/does-magma-use-a-standard-p-modular-system>), but I got no answer and no comment. 


Thank you very much for any help.


**Edit:**


\*See pages 305-307 of <https://books.google.de/books?id=VSZIBpYGwSMC&pg=PA315&lpg=PA315&dq=lux+pahlings+bruaer+characters&source=bl&ots=tjiXv1MYLC&sig=ACfU3U0HfCxHlCErPnMEnHRpxtwSEUccGw&hl=de&sa=X&ved=2ahUKEwif6uXzsc7iAhXB_KQKHX1cDWcQ6AEwDXoECAgQAQ#v=onepage&q=lux%20pahlings%20bruaer%20characters&f=false>


There, a bold $\mathbf{\zeta}\_m$ denotes the complex number $e^{\frac{2\pi i}{m}}$. Often, $m=p^n-1$.



Does MAGMA use a standard p-modular system?
Paragraph 3.2.1 of [On Certain Subgroups of $E\_8(2)$ and their Brauer Character Tables](https://www.research.manchester.ac.uk/portal/files/84018931/FULL_TEXT.PDF) explains precisely how the Brauer characters are defined in MAGMA. The ambiguity in the definition refers to the choice of a definite root of unity. MAGMA uses Conway polynomials for that purpose and from [page 306](https://books.google.de/books?id=VSZIBpYGwSMC&pg=PA306&lpg=PA306) of Lux and Pahlings I gather that they use the same convention.


