All modular forms of weight 2 can be expressed by Eisenstein series

Journal article, 2020

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 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.