Evaluation of the convolution sums _al+bm=n lσ(l) σ(m) with ab ≤ 9

The generating functions of divisor functions are quasimodular forms of weight 2 and their products belong to a space of quasimodular forms of higher weight. In this article, we evaluate the convolution sums_al+bm=nlσ(l)σ(m) sum_al+bm=n σ(l)σ(m) for all positive integers a, b and n with ab ≤ 9 and gcd(a, b) = 1.