Atlas › Modular forms › Weight 8 › Level 43 › 43.8.a

Newspace 43.8.a: $S_{8}^{\mathrm{new}}(\Gamma_0(43))$

Newforms

Label	Dim	Coefficient field	Trace form	AL signs	Sign	CM	Elliptic curve
43.8.a.a	11	degree 11	$11q - 24q^{2} - 68q^{3} + 602q^{4} - 752q^{5} - 681q^{6} - 12q^{7} + O(q^{8})$	−	$-1$
43.8.a.b	13	degree 13	$13q + 16q^{2} + 94q^{3} + 922q^{4} + 998q^{5} + 183q^{6} + 1360q^{7} + O(q^{8})$	+	$+1$

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 $T$
43.8.a.a	$x^{11} + 92x^{10} - 9481x^{9} - 727200x^{8} + 37572147x^{7} + 1848204432x^{6} - 71471199422x^{5} - 1493605134676x^{4} + 49298457987164x^{3} + 192562418140512x^{2} - 4321884204233064x + 10727646272486640$
43.8.a.b	$x^{13} - 110x^{12} - 14647x^{11} + 1644338x^{10} + 83647697x^{9} - 9040765014x^{8} - 238696796640x^{7} + 22147781872128x^{6} + 346543763033608x^{5} - 23407095660014208x^{4} - 213947978461547560x^{3} + 9098503326580908720x^{2} + 36787519140520780576x - 569654513316109811904$

Dimensions

Newforms $S_{8}^{\mathrm{new}}(\Gamma_0(43))$	24
Old forms	0
Cusp forms $S_{8}(\Gamma_0(43))$	24
Eisenstein series $E_{8}(\Gamma_0(43))$	2
Modular forms $M_{8}(\Gamma_0(43))$	26

Decomposition of the old subspace

The old subspace is 0.

Provenance

Stored in the atlas: computed by Sagebrush's modular symbols engine in 0.273 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, 43]: [1, 26] (certified at ell = 2147483647)
T = [(2, 1), (3, 1)]; h of degree 24 = 1 x 24 (phi(ord eps) x dim S_k^new); 6 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(43, 8)

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

cargo run --release -p sagebrush-web --example atlas -- 43:8 1000

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