Summary: In this paper, for the complex Lie algebra \({sl}_3 \) we propose an explicit formula for finding the multiplicity of the weight of the irreducible representation \( \Gamma_{\lambda} \), which is determined by its higher weight \( \lambda = (a, b) \). The set of all weights \( \Lambda \) of such a representation forms a group ring \( \mathbb{Z} [\Lambda] \) with the multiplicative basis \({e} (\mu), \mu \in \Lambda. \) The character of the representation \({\text{ Char}} \, \Gamma_{\lambda} \) is an element of \( \mathbb{Z} [\Lambda] \), the coefficients of which are the required multiplicities. The main idea of the calculations is to specify the basis \({e}(\mu) = x ^{\mu_1} y ^{\mu_2} \) of the group ring \( \mathbb{Z} [\lambda] \). This made it possible to represent the character \({\text{Char}} \, \Gamma_{\lambda} \) of the irreducible representation \( \Gamma_{\lambda} \) as a Schur polynomial \( s_{a, b} \left (x,{ y}/{x},{1}/{y} \right) \) of two variables \( x, y \). As a consequence, we express the coefficients of this polynomial through simple functions that are easily computed for linear time. The key role in the calculation was played by the explicitly found coefficients of the series decomposition \( \Delta ={1}/{\left ({y} ^{2} -x \right) \left (1- yx \right) \left (y-{x} ^{2} \right)}, \) in terms of the function \(c (n, k) = \min (n{-} k + 2, k)\){if } \(1 \leq k \leq n + 1\), and \(c (n, k) = 0\) otherwise.