Atlas › Modular forms › Weight 8 › Level 11 › 11.8.a

Newspace 11.8.a: $S_{8}^{\mathrm{new}}(\Gamma_0(11))$

Newforms

Label	Dim	Coefficient field	Trace form	AL signs	Sign	CM	Elliptic curve
11.8.a.a	2	$\mathbb{Q}(\sqrt{15})$	$2q - 8q^{2} - 6q^{3} - 104q^{4} - 470q^{5} - 696q^{6} - 1228q^{7} + O(q^{8})$	−	$-1$
11.8.a.b	4	degree 4	$4q - 35q^{3} + 604q^{4} + 537q^{5} + 1558q^{6} + 170q^{7} + O(q^{8})$	+	$+1$

Hecke characteristic polynomials

The eigenvalue of $T = T_{2} + T_{3}$ 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 $T$
11.8.a.a	$x^{2} + 14x - 1451$
11.8.a.b	$x^{4} + 35x^{3} - 6789x^{2} - 49545x + 101574$

Dimensions

Newforms $S_{8}^{\mathrm{new}}(\Gamma_0(11))$	6
Old forms	0
Cusp forms $S_{8}(\Gamma_0(11))$	6
Eisenstein series $E_{8}(\Gamma_0(11))$	2
Modular forms $M_{8}(\Gamma_0(11))$	8

Decomposition of the old subspace

The old subspace is 0.

Provenance

Stored in the atlas: computed by Sagebrush's modular symbols engine in 0.262 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, 11]: [1, 8] (certified at ell = 2147483171)
T = [(2, 1), (3, 1)]; h of degree 6 = 1 x 6 (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(11, 8)

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

cargo run --release -p sagebrush-web --example atlas -- 11:8 1000

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