Atlas › Modular forms › Weight 10 › Level 24 › 24.10.a

Newspace 24.10.a: $S_{10}^{\mathrm{new}}(\Gamma_0(24))$

Newforms

Label	Dim	Coefficient field	Trace form	AL signs
24.10.a.a	1	$\mathbb{Q}$	$q - 81q^{3} + 830q^{5} + 672q^{7} + O(q^{8})$	+
24.10.a.b	1	$\mathbb{Q}$	$q + 81q^{3} - 794q^{5} - 5880q^{7} + O(q^{8})$	−
24.10.a.c	1	$\mathbb{Q}$	$q + 81q^{3} + 614q^{5} + 2184q^{7} + O(q^{8})$	−
24.10.a.d	2	$\mathbb{Q}(\sqrt{109})$	$2q - 162q^{3} - 772q^{5} - 2880q^{7} + O(q^{8})$	+

Hecke characteristic polynomials

The eigenvalue of $T = T_{5} + T_{7}$ generates each orbit's coefficient field; on the newspace its characteristic polynomial factors over $\mathbb{Q}$ as one irreducible factor per orbit:

Orbit	Characteristic polynomial of $T$
24.10.a.a	$x - 1502$
24.10.a.b	$x + 6674$
24.10.a.c	$x - 2798$
24.10.a.d	$x^{2} + 3652x - 60956540$

Dimensions

Newforms $S_{10}^{\mathrm{new}}(\Gamma_0(24))$	5
Old forms	27
Cusp forms $S_{10}(\Gamma_0(24))$	32
Eisenstein series $E_{10}(\Gamma_0(24))$	8
Modular forms $M_{10}(\Gamma_0(24))$	40

Decomposition of the old subspace

$S_{10}^{\mathrm{old}}(\Gamma_0(24)) =$ $S_{10}^{\mathrm{new}}(\Gamma_0(2))^{\oplus 6}$ $\oplus$ $S_{10}^{\mathrm{new}}(\Gamma_0(3))^{\oplus 4}$ $\oplus$ $S_{10}^{\mathrm{new}}(\Gamma_0(4))^{\oplus 4}$ $\oplus$ $S_{10}^{\mathrm{new}}(\Gamma_0(6))^{\oplus 3}$ $\oplus$ $S_{10}^{\mathrm{new}}(\Gamma_0(8))^{\oplus 2}$ $\oplus$ $S_{10}^{\mathrm{new}}(\Gamma_0(12))^{\oplus 2}$

Provenance

Stored in the atlas: computed by Sagebrush's modular symbols engine in 0.325 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.

The engine's checks

dim M^+ at levels [1, 2, 3, 4, 6, 8, 12, 24]: [1, 3, 4, 6, 11, 11, 21, 40] (certified at ell = 2147483647)
T = [(5, 1), (7, 1)]; h of degree 5 = 1 x 5 (phi(ord eps) x dim S_k^new); 3 primes, 0 rejected

Open in the notebook · JSON · stored data

Recompute it yourself

In Sage mode at sagebrush.space (or npx sagebrush --sage):

newform_orbits(24, 10)

With the Rust engine (source), in engine/:

cargo run --release -p sagebrush-web --example atlas -- 24:10 1000

← 23.10.a · 25.10.a →