Atlas › Modular forms › Weight 8 › Level 47 › 47.8.a

Newspace 47.8.a: $S_{8}^{\mathrm{new}}(\Gamma_0(47))$

Newforms

Label	Dim	Coefficient field	Trace form	AL signs	Sign	CM	Elliptic curve
47.8.a.a	11	degree 11	$11q - 17q^{2} - 68q^{3} + 485q^{4} - 56q^{5} - 992q^{6} - 2256q^{7} + O(q^{8})$	−	$-1$
47.8.a.b	16	degree 16	$16q + 15q^{2} + 40q^{3} + 1125q^{4} + 444q^{5} - 128q^{6} + 1860q^{7} + O(q^{8})$	+	$+1$

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 $T$
47.8.a.a	$x^{11} + 85x^{10} - 11396x^{9} - 776664x^{8} + 49741911x^{7} + 2199688997x^{6} - 94915166122x^{5} - 1946034505916x^{4} + 64033249957883x^{3} + 292047342823529x^{2} - 3552085556855880x - 886277305483956$
47.8.a.b	$x^{16} - 55x^{15} - 25935x^{14} + 1076227x^{13} + 282916538x^{12} - 7798781507x^{11} - 1646865483912x^{10} + 24377050010755x^{9} + 5364546862289334x^{8} - 24374516395924541x^{7} - 9488679642127527088x^{6} - 22232369033877521159x^{5} + 8443102437779313561741x^{4} + 48715246409229699937466x^{3} - 3256621975957581031146953x^{2} - 15014623430239403913789432x + 473419371800796159567608964$

Dimensions

Newforms $S_{8}^{\mathrm{new}}(\Gamma_0(47))$	27
Old forms	0
Cusp forms $S_{8}(\Gamma_0(47))$	27
Eisenstein series $E_{8}(\Gamma_0(47))$	2
Modular forms $M_{8}(\Gamma_0(47))$	29

Decomposition of the old subspace

The old subspace is 0.

Provenance

Stored in the atlas: computed by Sagebrush's modular symbols engine in 0.277 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, 47]: [1, 29] (certified at ell = 2147483137)
T = [(2, 1), (3, 1)]; h of degree 27 = 1 x 27 (phi(ord eps) x dim S_k^new); 7 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(47, 8)

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

cargo run --release -p sagebrush-web --example atlas -- 47:8 1000

← 46.8.a · 48.8.a →