Atlas › Modular forms › Weight 6 › Level 23 › 23.6.a

Newspace 23.6.a: $S_{6}^{\mathrm{new}}(\Gamma_0(23))$

Newforms

Label	Dim	Coefficient field	Trace form	AL signs	Sign	CM	Elliptic curve
23.6.a.a	3	degree 3	$3q - 4q^{2} - 20q^{3} + 16q^{4} - 58q^{5} - 230q^{6} - 282q^{7} + O(q^{8})$	+	$-1$
23.6.a.b	6	degree 6	$6q + 4q^{2} + 16q^{3} + 112q^{4} + 42q^{5} + 367q^{6} + 300q^{7} + O(q^{8})$	−	$+1$

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 $T$
23.6.a.a	$x^{3} + 24x^{2} + 37x + 2$
23.6.a.b	$x^{6} - 20x^{5} - 1429x^{4} + 25977x^{3} + 395038x^{2} - 9385685x + 43074950$

Dimensions

Newforms $S_{6}^{\mathrm{new}}(\Gamma_0(23))$	9
Old forms	0
Cusp forms $S_{6}(\Gamma_0(23))$	9
Eisenstein series $E_{6}(\Gamma_0(23))$	2
Modular forms $M_{6}(\Gamma_0(23))$	11

Decomposition of the old subspace

The old subspace is 0.

Provenance

Stored in the atlas: computed by Sagebrush's modular symbols engine in 0.214 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, 23]: [1, 11] (certified at ell = 2147483647)
T = [(2, 1), (3, 1)]; h of degree 9 = 1 x 9 (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(23, 6)

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

cargo run --release -p sagebrush-web --example atlas -- 23:6 1000

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