= Weight-sixteen Eisenstein congruence
{title2=$[q^n](E_4\Delta)\equiv\sigma_{15}(n)\pmod{3617}$}
The weight-sixteen <cusp form> space is spanned by $E_4\Delta$. Its leading coefficient and the <Fourier expansion of a normalized Eisenstein series> give $3617E_{16}=3617E_4^4-3456000E_4\Delta$. The coefficient multiplier $-3456000$ is congruent to $16320$ modulo $3617$, and is invertible there. Coefficient comparison gives the displayed <modular congruence>. Integrality of $E_4\Delta$ follows from the <modular discriminant> product.
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