Every homomorphism SL(2,k) to SL(4,k) in positive characteristic is equivalent to one of 11 explicit matrix families, with four families common to all primes and additional families for p=2, p=3, and p at least 5.
Tanimoto, Exponential matrices, Linear Algebra Appl
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Homomorphisms from ${\rm SL}(2, k)$ to ${\rm SL}(4, k)$ in positive characteristic
Every homomorphism SL(2,k) to SL(4,k) in positive characteristic is equivalent to one of 11 explicit matrix families, with four families common to all primes and additional families for p=2, p=3, and p at least 5.