Atlas › Modular forms › Weight 4 › Level 43 › 43.4.a

Newspace 43.4.a: $S_{4}^{\mathrm{new}}(\Gamma_0(43))$

Newforms

Label	Dim	Coefficient field	Trace form	AL signs	Sign	CM	Elliptic curve
43.4.a.a	4	degree 4	$4q - 4q^{2} - 11q^{3} + 2q^{4} - 27q^{5} - 27q^{6} - 20q^{7} + O(q^{8})$	−	$-1$
43.4.a.b	6	degree 6	$6q + 6q^{2} + 7q^{3} + 22q^{4} + 43q^{5} - 3q^{6} + 8q^{7} + O(q^{8})$	+	$+1$

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 $T$
43.4.a.a	$x^{4} + 15x^{3} + 73x^{2} + 120x + 18$
43.4.a.b	$x^{6} - 13x^{5} - 69x^{4} + 1394x^{3} - 4594x^{2} - 156x + 11692$

Dimensions

Newforms $S_{4}^{\mathrm{new}}(\Gamma_0(43))$	10
Old forms	0
Cusp forms $S_{4}(\Gamma_0(43))$	10
Eisenstein series $E_{4}(\Gamma_0(43))$	2
Modular forms $M_{4}(\Gamma_0(43))$	12

Decomposition of the old subspace

The old subspace is 0.

Provenance

Stored in the atlas: computed by Sagebrush's modular symbols engine in 0.092 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, 12] (certified at ell = 2147483647)
T = [(2, 1), (3, 1)]; h of degree 10 = 1 x 10 (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(43, 4)

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

cargo run --release -p sagebrush-web --example atlas -- 43:4 1000

← 42.4.a · 44.4.a →