  We show that every elliptic modular form of integral weight greater than $1$
can be expressed as linear combinations of products of at most two cusp
expansions of Eisenstein series. This removes the obstruction of nonvanishing
central $\mathrm{L}$-values present in all previous work. For weights greater
than $2$, we refine our result further, showing that linear combinations of
products of exactly two cusp expansions of Eisenstein series suffice.
