Newspace 720.2.a: $S_{2}^{\mathrm{new}}(\Gamma_0(720))$

Newforms

Hecke characteristic polynomials

The eigenvalue of $T = T_{7} + 2T_{11} + 3T_{13} + 4T_{17} + 5T_{19} + 6T_{23} + 7T_{29} + 8T_{31} + 9T_{37} + 10T_{41} + 11T_{43} + 12T_{47} + 13T_{53} + 14T_{59} + 15T_{61} + 16T_{67}$ generates each orbit's coefficient field; on the newspace its characteristic polynomial factors over $\mathbb{Q}$ as one irreducible factor per orbit:

Dimensions

Decomposition of the old subspace

$S_{2}^{\mathrm{old}}(\Gamma_0(720)) =$ $S_{2}^{\mathrm{new}}(\Gamma_0(15))^{\oplus 10}$ $\oplus$ $S_{2}^{\mathrm{new}}(\Gamma_0(20))^{\oplus 9}$ $\oplus$ $S_{2}^{\mathrm{new}}(\Gamma_0(24))^{\oplus 8}$ $\oplus$ $S_{2}^{\mathrm{new}}(\Gamma_0(30))^{\oplus 8}$ $\oplus$ $S_{2}^{\mathrm{new}}(\Gamma_0(36))^{\oplus 6}$ $\oplus$ $S_{2}^{\mathrm{new}}(\Gamma_0(40))^{\oplus 6}$ $\oplus$ $S_{2}^{\mathrm{new}}(\Gamma_0(45))^{\oplus 5}$ $\oplus$ $S_{2}^{\mathrm{new}}(\Gamma_0(48))^{\oplus 4}$ $\oplus$ $S_{2}^{\mathrm{new}}(\Gamma_0(72))^{\oplus 4}$ $\oplus$ $S_{2}^{\mathrm{new}}(\Gamma_0(80))^{\oplus 3}$ $\oplus$ $S_{2}^{\mathrm{new}}(\Gamma_0(90))^{\oplus 4}$ $\oplus$ $S_{2}^{\mathrm{new}}(\Gamma_0(120))^{\oplus 4}$ $\oplus$ $S_{2}^{\mathrm{new}}(\Gamma_0(144))^{\oplus 2}$ $\oplus$ $S_{2}^{\mathrm{new}}(\Gamma_0(180))^{\oplus 3}$ $\oplus$ $S_{2}^{\mathrm{new}}(\Gamma_0(240))^{\oplus 2}$ $\oplus$ $S_{2}^{\mathrm{new}}(\Gamma_0(360))^{\oplus 2}$

Provenance

Stored in the atlas: computed by Sagebrush's modular symbols engine in 2.772 s (one thread) and proven: the dimensions are certified, and the characteristic polynomial of $T$ over $\mathbb{Z}$ is reconstructed by CRT past a rigorous coefficient bound.

newform_orbits(720, 2)

cargo run --release -p sagebrush-web --example atlas -- 720:2 1000

← 719.2.a · 721.2.a →