From: Convolution identities for twisted Eisenstein series and twisted divisor functions
Convolution sum
t 8 (N)
∑ m = 1 4 N − 1 σ 1 (m) σ 1 (4N−m)
1 12 {5 σ 3 (4N)+(1−24N) σ 1 (4N)}
∑ m = 1 2 N σ 1 (2m−1) σ 1 (4N−(2m−1))
σ 3 ∗ (2N)
t 8 (2N−1)
∑ m = 1 4 ∤ m 4 N − 1 σ 1 (m) σ 1 (4N−m)
σ 3 ∗ (2N)+ σ 3 ∗ (2N;4)
17 t 8 (N−1)
∑ m = 1 mod 4 m ≡ 2 mod 4 4 N − 1 σ 1 (m) σ 1 (4N−m)
σ 3 ∗ (2N;4)
9 t 8 (N−1)