acb_theta_g2_even_weight
Synopsis
#include <flint/acb_theta.h>The formulas are those of [Str2014, §7.1], normalised as \psi_4 = h_4/4, \psi_6 = h_6/4, \chi_{10} = -2^{-12} h_{10} and \chi_{12} = 2^{-15}h_{12}, so that the Fourier expansions begin
\begin{aligned}
\psi_4(\tau) &= 1 + 240(q_1 + q_3) + \cdots, &
\psi_6(\tau) &= 1 - 504(q_1 + q_3) + \cdots, \\
\chi_{10}(\tau) &= (q_2 - 2 + q_2^{-1}) q_1 q_3 + \cdots, &
\chi_{12}(\tau) &= (q_2 + 10 + q_2^{-1}) q_1 q_3 + \cdots.
\end{aligned}
\chi_{10} and \chi_{12} differ from Igusa's [Igu1979] by constant factors.
References#
- [Str2014] M. Streng, "Computing Igusa class polynomials", Math. Comp. 83:285 (2014), 275–309. https://doi.org/10.1090/S0025-5718-2013-02712-3
- [Igu1979] J.-I. Igusa, "On the ring of modular forms of degree two over Z", Amer. J. Math. 101:1 (1979), 149–183. https://doi.org/10.2307/2373943
Cite this page
The FLINT team, “acb_theta_g2_even_weight (acb_theta.h),” FLINT: Fast Library for Number Theory, documentation, version 3.7.0-dev, 2026. https://flintlib.org/doc/acb_theta/acb_theta_g2_even_weight.html (generated 2026-10-20).
@misc{flint-doc-acb-theta-acb-theta-g2-even-weight,
author = {{The FLINT team}},
title = {{acb\_theta\_g2\_even\_weight (acb\_theta.h)}},
howpublished = {FLINT: Fast Library for Number Theory, documentation, version 3.7.0-dev},
year = {2026},
url = {https://flintlib.org/doc/acb_theta/acb_theta_g2_even_weight.html},
note = {Generated 2026-10-20}
}