Eisenstein Series and Convolution Sums

We compute Fourier series expansions of weight $2$ and weight $4$ Eisenstein series at various cusps. Then we use results of these computations to give formulas for the convolution sums ${\sum }_{a+pb=n}\sigma (a)\sigma (b)$, ${\sum }_{p_{1}a+p_{2}b=n}\sigma (a)\sigma (b)$ and $ \sum_{a+p_1 p_2 b=n}\sigma(a)\sigma(b)$where$p, p_1, p_2$ are primes.