Add generic character table for SL(2,q), with q odd and non-square?

[fingolfin]

There may be good reasons this is not in here: e.g. it may not fit into the data format. Or it is not as useful due to the exceptions. Or whatever. But it might be worth figuring out...

That said, the table cane be found on page 58 (Table 5.4) in

Cédric Bonnafé, Representations of $\mathrm{SL}_2(\mathbb{F}_q)$, https://doi.org/10.1007/978-0-85729-157-8

[SoongNoonien]

Maybe I'm missing something but we have SL2.1, isn't that what you are looking for?

[fingolfin]

I think SL2.1 only covers the case $\mathrm{SL}_2(q^2)$ and $q$ odd, i.e. over fields of square size.

I adjusted the title to clarify that the missing case is $q$ odd and not a square.

[fingolfin]

That said, in SL2.0 it indeed says:

See SL2.1 for the generic character table of $SL_2(q)$, $q$ odd

[SoongNoonien]

In the info string of SL2.1 it says:

Information about the generic character table of $SL_2(q^2)$,
$q^2$ odd. The possible values for q are given by
$q^2 = p^m$ with m a non negative integer and $p$ a prime number.

I think it's $q^2$ to avoid $\sqrt{q}$ in the table.