Atlas › Modular forms › Weight 6 › Level 43 › 43.6.a

Newspace 43.6.a: $S_{6}^{\mathrm{new}}(\Gamma_0(43))$

Newforms

Label	Dim	Coefficient field	Trace form	AL signs	Sign	CM	Elliptic curve
43.6.a.a	8	degree 8	$8q - 12q^{2} - 26q^{3} + 122q^{4} - 212q^{5} - 69q^{6} - 136q^{7} + O(q^{8})$	+	$-1$
43.6.a.b	10	degree 10	$10q + 8q^{2} + 28q^{3} + 202q^{4} + 138q^{5} + 75q^{6} + 60q^{7} + O(q^{8})$	−	$+1$

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 $T$
43.6.a.a	$x^{8} + 38x^{7} - 643x^{6} - 23394x^{5} + 75089x^{4} + 3165034x^{3} - 4442068x^{2} - 72841260x + 174248300$
43.6.a.b	$x^{10} - 36x^{9} - 1581x^{8} + 63696x^{7} + 677991x^{6} - 36557436x^{5} - 13798070x^{4} + 7363887672x^{3} - 23134329540x^{2} - 372569030352x + 677983951440$

Dimensions

Newforms $S_{6}^{\mathrm{new}}(\Gamma_0(43))$	18
Old forms	0
Cusp forms $S_{6}(\Gamma_0(43))$	18
Eisenstein series $E_{6}(\Gamma_0(43))$	2
Modular forms $M_{6}(\Gamma_0(43))$	20

Decomposition of the old subspace

The old subspace is 0.

Provenance

Stored in the atlas: computed by Sagebrush's modular symbols engine in 0.223 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, 20] (certified at ell = 2147483647)
T = [(2, 1), (3, 1)]; h of degree 18 = 1 x 18 (phi(ord eps) x dim S_k^new); 4 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, 6)

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

cargo run --release -p sagebrush-web --example atlas -- 43:6 1000

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