Atlas › Modular forms › Weight 10 › Level 11 › 11.10.a

Newspace 11.10.a: $S_{10}^{\mathrm{new}}(\Gamma_0(11))$

Newforms

Label	Dim	Coefficient field	Trace form	AL signs	Sign	CM	Elliptic curve
11.10.a.a	3	degree 3	$3q - 186q^{3} + 912q^{4} - 1824q^{5} - 10956q^{6} - 7260q^{7} + O(q^{8})$	+	$-1$
11.10.a.b	5	degree 5	$5q + 16q^{2} + 112q^{3} + 708q^{4} + 1594q^{5} + 10378q^{6} + 8400q^{7} + O(q^{8})$	−	$+1$

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 $T$
11.10.a.a	$x^{3} + 186x^{2} - 9771x + 82744$
11.10.a.b	$x^{5} - 128x^{4} - 90422x^{3} + 9377514x^{2} + 1528897329x - 38333773422$

Dimensions

Newforms $S_{10}^{\mathrm{new}}(\Gamma_0(11))$	8
Old forms	0
Cusp forms $S_{10}(\Gamma_0(11))$	8
Eisenstein series $E_{10}(\Gamma_0(11))$	2
Modular forms $M_{10}(\Gamma_0(11))$	10

Decomposition of the old subspace

The old subspace is 0.

Provenance

Stored in the atlas: computed by Sagebrush's modular symbols engine in 0.284 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, 10] (certified at ell = 2147483171)
T = [(2, 1), (3, 1)]; h of degree 8 = 1 x 8 (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(11, 10)

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

cargo run --release -p sagebrush-web --example atlas -- 11:10 1000

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