FLINT3.7.0-dev
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acb_theta_g2_chi3_6

Synopsis#include <flint/acb_theta.h>
void acb_theta_g2_chi3_6(acb_poly_t res, acb_srcptr dth, slong prec)source

Sets res to the vector-valued cusp form χ3,6\chi_{3,6} of weight det⁡3⊗Sym6\det^3\otimes \mathrm{Sym}^6 with character, given the first derivatives dth of all 16 theta functions at z=0z = 0 (as computed by acb_theta_jet with ord = 1 and all set) [CFG2017]: χ3,6(τ)=164π6∏(a,b) odd(∂θa,b∂z1(0,τ)x1+∂θa,b∂z2(0,τ)x2)\chi_{3,6}(\tau) = \frac{1}{64\pi^6} \prod_{(a,b) \text{ odd}} \left(\frac{\partial \theta_{a,b}}{\partial z_1}(0,\tau) x_1 + \frac{\partial\theta_{a,b}}{\partial z_2}(0,\tau) x_2\right).

References#

  • [CFG2017] F. Cléry, C. Faber, and G. van der Geer. "Covariants of binary sextics and vector-valued Siegel modular forms of genus two", Math. Ann. 369 (2017), 1649–1669. https://doi.org/10.1007/s00208-016-1510-2
Cite this page

The FLINT team, “acb_theta_g2_chi3_6 (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_chi3_6.html (generated 2026-11-02).