Weight-four modular forms on Gamma 0 3
= Weight-four modular forms on Gamma 0 3
{title2=$M_4(\Gamma_0(3))=\mathbb C E_4(z)\oplus\mathbb C E_4(3z)$}
The group $\Gamma_0(3)$ has index four. The <dimension bound for modular forms on a finite-index subgroup> gives dimension at most two in weight four. The <Eisenstein series> $E_4(z)$ and its <oldform by argument dilation> $E_4(3z)$ are independent, since their constant coefficients agree while their $q$ coefficients are $240$ and zero.