Atlas › Modular forms › Weight 6 › Level 47 › 47.6.a

Newspace 47.6.a: $S_{6}^{\mathrm{new}}(\Gamma_0(47))$

Newforms

Label	Dim	Coefficient field	Trace form	AL signs	Sign	CM	Elliptic curve
47.6.a.a	7	degree 7	$7q - 9q^{2} - 20q^{3} + 53q^{4} - 58q^{5} - 32q^{6} - 236q^{7} + O(q^{8})$	+	$-1$
47.6.a.b	12	degree 12	$12q + 7q^{2} + 16q^{3} + 213q^{4} + 42q^{5} + 112q^{6} + 352q^{7} + O(q^{8})$	−	$+1$

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 $T$
47.6.a.a	$x^{7} + 29x^{6} - 601x^{5} - 13429x^{4} + 83355x^{3} + 1390049x^{2} - 3319032x - 10267716$
47.6.a.b	$x^{12} - 23x^{11} - 2276x^{10} + 45314x^{9} + 1866389x^{8} - 31980858x^{7} - 676169549x^{6} + 9716033175x^{5} + 101210907638x^{4} - 1122526657354x^{3} - 3769953988577x^{2} + 13345867482952x - 8726123100764$

Dimensions

Newforms $S_{6}^{\mathrm{new}}(\Gamma_0(47))$	19
Old forms	0
Cusp forms $S_{6}(\Gamma_0(47))$	19
Eisenstein series $E_{6}(\Gamma_0(47))$	2
Modular forms $M_{6}(\Gamma_0(47))$	21

Decomposition of the old subspace

The old subspace is 0.

Provenance

Stored in the atlas: computed by Sagebrush's modular symbols engine in 0.226 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, 21] (certified at ell = 2147483137)
T = [(2, 1), (3, 1)]; h of degree 19 = 1 x 19 (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(47, 6)

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

cargo run --release -p sagebrush-web --example atlas -- 47:6 1000

← 46.6.a · 48.6.a →