Atlas › Modular forms › Weight 10 › Level 14 › 14.10.a

Newspace 14.10.a: $S_{10}^{\mathrm{new}}(\Gamma_0(14))$

Newforms

Label	Dim	Coefficient field	Trace form	AL signs	Sign
14.10.a.a	1	$\mathbb{Q}$	$q - 16q^{2} - 6q^{3} + 256q^{4} + 560q^{5} + 96q^{6} - 2401q^{7} + O(q^{8})$	+ +	$-1$
14.10.a.b	1	$\mathbb{Q}$	$q + 16q^{2} + 170q^{3} + 256q^{4} + 544q^{5} + 2720q^{6} - 2401q^{7} + O(q^{8})$	− +	$+1$
14.10.a.c	2	$\mathbb{Q}(\sqrt{2305})$	$2q - 32q^{2} - 14q^{3} + 512q^{4} - 2730q^{5} + 224q^{6} + 4802q^{7} + O(q^{8})$	+ −	$+1$

Hecke characteristic polynomials

The eigenvalue of $T = T_{3} + 3T_{5}$ 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 $T$
14.10.a.a	$x - 1674$
14.10.a.b	$x - 1802$
14.10.a.c	$x^{2} + 8204x + 6168084$

Dimensions

Newforms $S_{10}^{\mathrm{new}}(\Gamma_0(14))$	4
Old forms	12
Cusp forms $S_{10}(\Gamma_0(14))$	16
Eisenstein series $E_{10}(\Gamma_0(14))$	4
Modular forms $M_{10}(\Gamma_0(14))$	20

Decomposition of the old subspace

$S_{10}^{\mathrm{old}}(\Gamma_0(14)) =$ $S_{10}^{\mathrm{new}}(\Gamma_0(2))^{\oplus 2}$ $\oplus$ $S_{10}^{\mathrm{new}}(\Gamma_0(7))^{\oplus 2}$

Provenance

Stored in the atlas: computed by Sagebrush's modular symbols engine in 0.294 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]: [1, 3, 7, 20] (certified at ell = 2147483647)
T = [(3, 1), (5, 3)]; h of degree 4 = 1 x 4 (phi(ord eps) x dim S_k^new); 2 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, 10)

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

cargo run --release -p sagebrush-web --example atlas -- 14:10 1000

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