A global code for the character table of PSL(2,q)

Question

We can easily get the character table of $\mathrm{PSL}(2,q)$ for some fixed small prime power $q$, we can just do (for example):

gap> Display(CharacterTable(PSL(2,q)));

I don't know how the software is doing, I guess it uses some Atlas database for $q$ small enough or computes directly. The point is that there exists a global understanding of the character table of $\mathrm{PSL}(2,q)$, see for example Section 5.2 in Fulton & Harris, or page 12 in this note of J. Adams (up to typos). I need a code computing this character table following this global understanding (in order to interpolate it for $q$ non prime-power, see why here). I tried to write it myself but I got troubles with some ambiguities. I asked J. Adams but he does not have such a code. Now this global understanding is a well-known result, so the code I am looking for should already exist somewhere (in the source of some software, or as a private material).

Question: If you have such a code (that you would be willing to share), could you put it as an answer of this post?
Otherwise, if you know somewhere (or someone) susceptible to have such a code, could you please mention it (or her/him)?

Remark: My laptop needed 5min36s to compute the following:

gap> Display(CharacterTable(PSL(2,163)));

whereas it should be instantaneous be above global understanding. So the computation of the character table of $\mathrm{PSL}(2,q)$ is suboptimal on gap, and the expected global code would fix that.

Answer 1

The quickest way to display the character table for a fixed prime-power $q$ is:

Display(CharacterTable( "PSL", 2, q)

The generic character table is in fact available on GAP4 (as pointed out in private by Frank Lübeck) with the following commands:

For $q$ even:

gap> Print(CharacterTableFromLibrary("SL2even"));

For $q \equiv 1 \mod 4$:

gap> Print(CharacterTableFromLibrary("PSL2even"));

For $q \equiv 3 \mod 4$:

gap> Print(CharacterTableFromLibrary("PSL2odd"));