For v_p(a_p) > floor((k-1)/p), the semisimple mod p reduction of the crystalline representation V_{k,a_p} is V_{k,0}.
Reductions of modular Galois representations of Slope (2,3)
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We compute the semisimplifications of the mod-$p$ reductions of $2$-dimensional crystalline representations of the absolute Galois group of the p-adic numbers of slope $(2,3)$ and arbitrary weight, building on work of Bhattacharya-Ghate
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Reductions of some two-dimensional crystalline representations via Kisin modules
For v_p(a_p) > floor((k-1)/p), the semisimple mod p reduction of the crystalline representation V_{k,a_p} is V_{k,0}.