The Explicit Hypergeometric Modularity Calculator

My dissertation was based on the Explicit Hypergeometric Modularity Method (EHMM), introduced initially by Michael Allen, Brian Grove, Ling Long, and Fang-Ting Tu.  In collaboration with the original authors, we have created the EHMM calculator. The calculator computes the basic hypergeometric information important in the EHMM papers, including the values of finite field hypergeometric series that are not defined over Q, zigzag diagrams, and other useful data. The calculator can also be used to construct the modular forms described in the sequence of papers listed below. We hope that calculator will be useful for research and mentoring for those working on hypergeometric series and other formal power series. Please email esmerosen [at] gmail [dot] com if you notice any bugs or if you have any other questions. 

This page is the up to date version for the calculator; this website is no longer updated. See these slides for a short demonstration of how to use the calculator.

Sage files

 Documentation  file

Papers using the EHMM

• The Explicit Hypergeometric Modularity Method I, by Allen, Grove, Long, and Tu, Adv. in Math. 478 (2025), arxiv:2404.00711

• The Explicit Hypergeometric Modularity Method II, by Allen, Grove, Long, and Tu, Res. Math. Sci. 12 (2025), arxiv:2411.15116

• L-values of certain weight 3 modular forms and transformations of hypergeometric series, by Rosen, Res. Math Sci. 13 (2026), arXiv:2412.07054

• Modular forms and certain 2F1(1) hypergeometric series, by Rosen, Proc. Amer. Math. Soc. 154 (2026), arXiv:2502.08760

• On some hypergeometric modularity conjectures of Dawsey and McCarthy, by Grove, preprint (2025), arXiv:2507.19971

• Explicit hypergeometric modularity of certain weight two and four Hecke eigenforms, by Maity and Barman, preprint (2026), arXiv:2604.02723

• The Explicit Hypergeometric Modularity Method III, by Grove, Long, Rosen, and Tu, in preparation (not yet implemented)

• Explicit Modularity of reducible rank 2 hypergeometric motives I, by Rosen, in preparation

• Explicit Modularity of reducible rank 2 hypergeometric motives II, by Rosen, in preparation

Zigzag diagrams (above) and p-adic orders of coefficients of a hypergeometric series (below) found using the EHMM calculator