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$\operatorname{SL}_2(q)$, part II
We compute the trivial source character tables (also called species tables of the trivial source ring) of the infinite family of finite groups 
$\operatorname{SL}_{2}(q)$ for q even over a large enough field of odd characteristics. This article is a continuation of our article Trivial Source Character Tables of 
$\operatorname{SL}_{2}(q)$, where we considered, in particular, the case in which q is odd in non-defining characteristic.
Let 
${\rm\Delta}:G\rightarrow \text{GL}(n,K)$ be an absolutely irreducible representation of an arbitrary group 
$G$ over an arbitrary field 
$K$; let 
${\it\chi}:G\rightarrow K:g\mapsto \text{tr}({\rm\Delta}(g))$ be its character. In this paper, we assume knowledge of 
${\it\chi}$ only, and study which properties of 
${\rm\Delta}$ can be inferred. We prove criteria to decide whether 
${\rm\Delta}$ preserves a form, is realizable over a subfield, or acts imprimitively on 
$K^{n\times 1}$. If 
$K$ is finite, we can decide whether the image of 
${\rm\Delta}$ belongs to certain Aschbacher classes.
