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We find bases for the spaces$M_2\Big(\Gamma_0(24),\Big(\frac{d}{\cdot}\Big)\Big)$ ($d=1,8,12, 24$) ofmodular forms. We determine the Fourier coefficients of all $35$ theta products$\varphi[a_1,a_2,a_3,a_4](z)$ in these spaces. We then deduce formulas for thenumber of representations of a positive integer $n$ by diagonal quaternaryquadratic forms with coefficients $1$, $2$, $3$ or $6$ in a uniform manner, ofwhich $14$ are Ramanujan's universal quaternary quadratic forms. We also findall the eta quotients in the Eisenstein spaces$E_2\Big(\Gamma_0(24),\Big(\frac{d}{\cdot}\Big)\Big)$ ($d=1,8,12,24$) and givetheir Fourier coefficients.

Theta Products and Eta Quotients of Level $24$ and Weight $2$