= Weight-four Eisenstein basis at level two
{title2=$M_4(\Gamma_0(2))=\mathbb C E_4(\tau)\oplus\mathbb C E_4(2\tau)$}
There are no weight-four <cusp forms> at level two. A nonzero form would have a weight-twelve <coset norm of a modular form> with <modular cusp> order at least two, contradicting the simple <modular cusp> order and interior nonvanishing of the <modular discriminant>. The two independent displayed <Eisenstein series> span the weight-four space, since its cusp-constant map embeds it in a two-dimensional space.
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