Atlas › Modular forms › Weight 12 › Level 14 › 14.12.a

Newspace 14.12.a: $S_{12}^{\mathrm{new}}(\Gamma_0(14))$

Newforms

Label	Dim	Coefficient field	Trace form	AL signs	Sign
14.12.a.a	1	$\mathbb{Q}$	$q - 32q^{2} - 396q^{3} + 1024q^{4} + 7350q^{5} + 12672q^{6} + 16807q^{7} + O(q^{8})$	+ −	$-1$
14.12.a.b	1	$\mathbb{Q}$	$q + 32q^{2} - 90q^{3} + 1024q^{4} - 7480q^{5} - 2880q^{6} - 16807q^{7} + O(q^{8})$	− +	$-1$
14.12.a.c	2	$\mathbb{Q}(\sqrt{153169})$	$2q - 64q^{2} + 350q^{3} + 2048q^{4} + 266q^{5} - 11200q^{6} - 33614q^{7} + O(q^{8})$	+ +	$+1$
14.12.a.d	2	$\mathbb{Q}(\sqrt{352969})$	$2q + 64q^{2} - 350q^{3} + 2048q^{4} + 3738q^{5} - 11200q^{6} + 33614q^{7} + O(q^{8})$	− −	$+1$

Hecke characteristic polynomials

The eigenvalue of $T = T_{3} + T_{5}$ 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 $T$
14.12.a.a	$x - 6954$
14.12.a.b	$x + 7570$
14.12.a.c	$x^{2} - 616x - 74038932$
14.12.a.d	$x^{2} - 3388x - 2777868$

Dimensions

Newforms $S_{12}^{\mathrm{new}}(\Gamma_0(14))$	6
Old forms	14
Cusp forms $S_{12}(\Gamma_0(14))$	20
Eisenstein series $E_{12}(\Gamma_0(14))$	4
Modular forms $M_{12}(\Gamma_0(14))$	24

Decomposition of the old subspace

$S_{12}^{\mathrm{old}}(\Gamma_0(14)) =$ $S_{12}^{\mathrm{new}}(\Gamma_0(1))^{\oplus 4}$ $\oplus$ $S_{12}^{\mathrm{new}}(\Gamma_0(7))^{\oplus 2}$

Provenance

Stored in the atlas: computed by Sagebrush's modular symbols engine in 0.341 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, 7, 14]: [2, 4, 9, 24] (certified at ell = 2147483647)
T = [(3, 1), (5, 1)]; h of degree 6 = 1 x 6 (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(14, 12)

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

cargo run --release -p sagebrush-web --example atlas -- 14:12 1000

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