  Let $0< n,\alpha,\beta\in\mathbb{N}$ be such that $\gcd{(\alpha,\beta)}=1$.
We carry out the evaluation of the convolution sums $\underset{\substack{
{(k,l)\in\mathbb{N}^{2}} \\ {\alpha\,k+\beta\,l=n} }
}{\sum}\sigma(k)\sigma_{3}(l)$ and $\underset{\substack{
{(k,l)\in\mathbb{N}^{2}} \\ {\alpha\,k+\beta\,l=n} }
}{\sum}\sigma_{3}(k)\sigma(l)$ for all levels $\alpha\beta\in\mathbb{N}$, by
using in particular modular forms. We next apply convolution sums belonging to
this class of levels to determine formulae for the number of representations of
a positive integer $n$ by the quadratic forms in twelve variables
$\underset{i=1}{\overset{12}{\sum}}x_{i}^{2}$ when the level $\alpha\beta\equiv
0\pmod{4}$, and $\underset{i=1}{\overset{6}{\sum}}\,(\,x_{2i-1}^{2}+
x_{2i-1}x_{2i} + x_{2i}^{2}\,)$ when the level $\alpha\beta\equiv 0\pmod{3}$.
Our approach is then illustrated by explicitly evaluating the convolution sum
for $\alpha\beta=3$, $4$, $6$, $7$, $8$, $9$, $12$, $14$, $15$, $16$, $18$,
$20$, $21$, $27$, $32$. These convolution sums are then applied to determine
explicit formulae for the number of representations of a positive integer $n$
by quadratic forms in twelve variables.
