Strange character parameter restrictions

[fingolfin]

julia> T = genchartab("SL3.n1");

julia> printcharparam(T)
1
2
3
4	n ∈ {1,…, q - 1} except 1//(q - 1)*n ∈ ℤ
5	n ∈ {1,…, q - 1} except 1//(q - 1)*n ∈ ℤ
6	n ∈ {1,…, q - 1}, m ∈ {1,…, q - 1} except 1//(q - 1)*m - 1//(q - 1)*n ∈ ℤ
7	n ∈ {1,…, q^2 - 1} except 1//(q + 1)*n ∈ ℤ
8	n ∈ {1,…, q^2 + q + 1} except 1//(q^2 + q + 1)*n ∈ ℤ
9
10

So for character 4, the value of $n$ must satisfy $1\leq n\leq q-1$ and $(q-1) \nmid n$ -- that seems like a convoluted way of saying $1\leq n\leq q-2$.

Am I missing something? Perhaps there are deeper theoretical or algorithmic reasons why it is being expressed like this? Or maybe it's just an artifact of how the data was generated? Or...?

[SoongNoonien]

I think the reason for this is that these parameters are only unique up to congruence. The character obtained by setting n equal to for example 3 is the same as the one obtained by setting n equal to 3+q-1. So the parameter ranges are specified in this way that one is still able to see the original modulus.

In this case it would even be functionally equivalent to write n ∈ {0,…, q - 2} except 1//(q - 1)*n ∈ ℤ. Frank Lübeck (and me as well) would prefer this because this would be more in line with charsums and classsums. Ideally these sum functions can be automated by using the parameter ranges sometime.