English

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

Number Theory 2019-08-13 v1

Abstract

We show that every elliptic modular form of integral weight greater than 11 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\mathrm{L}-values present in all previous work. For weights greater than 22, we refine our result further, showing that linear combinations of products of exactly two cusp expansions of Eisenstein series suffice.

Keywords

Cite

@article{arxiv.1908.03616,
  title  = {All modular forms of weight 2 can be expressed by Eisenstein series},
  author = {Martin Raum and Jiacheng Xia},
  journal= {arXiv preprint arXiv:1908.03616},
  year   = {2019}
}