Atlas › Modular forms › Weight 8 › Level 23 › 23.8.a

Newspace 23.8.a: $S_{8}^{\mathrm{new}}(\Gamma_0(23))$

Newforms

Label	Dim	Coefficient field	Trace form	AL signs	Sign	CM	Elliptic curve
23.8.a.a	5	degree 5	$5q - 16q^{2} - 68q^{3} + 256q^{4} - 56q^{5} + 538q^{6} - 1156q^{7} + O(q^{8})$	−	$-1$
23.8.a.b	8	degree 8	$8q + 40q^{3} + 640q^{4} + 444q^{5} - 1745q^{6} + 1446q^{7} + O(q^{8})$	+	$+1$

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 $T$
23.8.a.a	$x^{5} + 84x^{4} - 1828x^{3} - 185902x^{2} - 3013037x - 13403350$
23.8.a.b	$x^{8} - 40x^{7} - 13974x^{6} + 575357x^{5} + 60679903x^{4} - 2143447954x^{3} - 107780594736x^{2} + 2281129020221x + 76387113833190$

Dimensions

Newforms $S_{8}^{\mathrm{new}}(\Gamma_0(23))$	13
Old forms	0
Cusp forms $S_{8}(\Gamma_0(23))$	13
Eisenstein series $E_{8}(\Gamma_0(23))$	2
Modular forms $M_{8}(\Gamma_0(23))$	15

Decomposition of the old subspace

The old subspace is 0.

Provenance

Stored in the atlas: computed by Sagebrush's modular symbols engine in 0.256 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, 15] (certified at ell = 2147483647)
T = [(2, 1), (3, 1)]; h of degree 13 = 1 x 13 (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(23, 8)

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

cargo run --release -p sagebrush-web --example atlas -- 23:8 1000

← 22.8.a · 24.8.a →