extended for a wider class of modules for $\mathfrak{sl}_2[t]$, which are indexed by partitions and are known in the literature as fusion products [@FL99]. They generalize many known families of representations for $\mathfrak{sl}_2[t]$, e.g. stable Demazure modules [@CV13 Theorem 2], local Weyl modules [@CP01] and tuncated Weyl modules [@KL15 Theorem 4.3]. Under a suitable condition on the partition, fusion products admit a level $m$–Demazure flag [@CSSW14 Theorem 3.3] and recurrence relations were established in the same paper. A closed form solution of these recurrences was however, only obtained in very special cases (see Remark \[rem21\]). It turned out that in these special cases there is a beautiful link between these modules and number theory and combinatorics: numerical multiplicities are closely related to Chebyshev polynomials [@BCSV15 Corollary 1.3], several specializations of the generting series associated to the graded multiplicities specialize to Ramanujan’s fifth order mock theta functions [@BCSV15 Theorem 1.6.], certain weighted versions of the generating series give Carlitz q–Fibonacci polynomials [@BCK16 Proposition 2.5.3] and are limits of hypergeometric series [@BCK16 Section 2.5.4]. One of the motivations of the present paper is to complete the results of [@BCSV15; @CSSW14] by finding a formula for the graded multiplicities in a level $m$–Demazure 