Context. The high degree of deuteration observed in some prestellar cores depends on the ortho-to-para H_{2_{ratio through the H fractionation.Aims. We want to constrain the ortho/para H_{2_{ratio across the L183 prestellar core. This is required to correctly describe the deuteration amplification phenomenon in depleted cores such as L183 and to relate the total (ortho+para) H_{2_{D^{+^{abundance to the sole ortho-H_{2_{D^{+^{column density measurement.Methods. To constrain this ortho/para H_{2_{ratio and derive its profile, we make use of the N_{2_{D^{+^{/N_{2_{H^{+^{ratio and of the ortho-H_{2_{D^{+^{observations performed across the prestellar core. We use two simple chemical models limited to an almost totally depleted core description. New dissociative recombination and trihydrogen cation-dihydrogen reaction rates (including all isotopologues) are presented in this paper and included in our models.Results. We estimate the H_{2_{D^{+^{ortho/para ratio in the L183 cloud, and constrain the H_{2_{ortho/para ratio: we show that it varies across the prestellar core by at least an order of magnitude, being still very high (≈0.1) in most of the cloud. Our time-dependent model indicates that the prestellar core is presumably older than 1.5-2 10^{5^{years but that it may not be much older. We also show that it has reached its present density only recently and that its contraction from a uniform density cloud can be constrained.Conclusions. A proper understanding of deuteration chemistry cannot be attained without taking into account the whole ortho/para family of molecular hydrogen and trihydrogen cation isotopologues as their relations are of utmost importance in the global scheme. Tracing the ortho/para H_{2_{ratio should also place useful constraints on the dynamical evolution of prestellar cores.}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}

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