Hecke Eigenform Product Identities for Full-Level Hilbert Modular Forms

@misc{chen2026hecke,
  title = {{Hecke Eigenform Product Identities for Full-Level Hilbert Modular Forms}},
  author = {Dijia Chen and Bowen Gan and Chao Qin and Yang Zhou},
  howpublished = {arXiv},
  year = {2026},
  month = oct,
  doi = {10.48550/arxiv.2610.12979},
  eprint = {2610.12979},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2610.12979},
}

TY  - UNPB
TI  - Hecke Eigenform Product Identities for Full-Level Hilbert Modular Forms
AU  - Dijia Chen
AU  - Bowen Gan
AU  - Chao Qin
AU  - Yang Zhou
PY  - 2026
DA  - 2026/10/09
PB  - arXiv
DO  - 10.48550/arxiv.2610.12979
UR  - https://arxiv.org/abs/2610.12979
AB  - We study full-level Hilbert Hecke eigenform product identities over totally real fields of degree at least two, allowing arbitrary compatible narrow class characters. Combining our results with previous work, we classify products of two Eisenstein eigenforms of positive parallel integral weights and products of an Eisenstein eigenform of weight at least two with a cuspidal eigenform of positive parallel integral weight. The unique identity in each of these two classes is given by E_4=60 E_2^2 and h_8=120 E_2 · h_6, respectively, both over ℚ(√5). The proofs use constant-term comparisons, indecomposable Fourier exponents, integrality of reciprocal Eisenstein constant terms, and a Rankin-Selberg formula for Petersson inner products. In the remaining case of a weight-one Eisenstein factor and a cuspidal factor, we also establish h_5=12E_1(1,ε)· h_4 over ℚ(√3), where ε is the nontrivial narrow class character. All eigenforms in these identities have unit-ideal coefficient one.
ER  -