From: Convolution identities for twisted Eisenstein series and twisted divisor functions
Convolution sums
∑ m = 1 L σ 1 (2m−1) σ 1 (2L−2m+1)= σ 3 ∗ (L)
∑ m = 1 L σ 1 (2m−1) σ 3 (2L−2m+1)= σ 5 ∗ (L)
∑ m = 1 2 L − 1 ( − 1 ) m + 1 σ 1 ∗ (m) σ 1 ∗ (2L−m)=L σ 1 ∗ (L)
∑ m = 1 2 L − 1 ( − 1 ) m + 1 σ 1 ∗ (m) σ 3 ∗ (2L−m)=L σ 3 ∗ (L)