Atlas › Modular forms › Weight 6 › Level 31 › 31.6.a

Newspace 31.6.a: $S_{6}^{\mathrm{new}}(\Gamma_0(31))$

Newforms

Label	Dim	Coefficient field	Trace form	AL signs	Sign	CM	Elliptic curve
31.6.a.a	5	degree 5	$5q - 9q^{2} - 20q^{3} + 53q^{4} - 72q^{5} - 144q^{6} - 108q^{7} + O(q^{8})$	+	$-1$
31.6.a.b	8	degree 8	$8q + 7q^{2} - 2q^{3} + 149q^{4} + 128q^{5} + 72q^{6} + 88q^{7} + O(q^{8})$	−	$+1$

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 $T$
31.6.a.a	$x^{5} + 29x^{4} + 112x^{3} - 2974x^{2} - 26304x - 55456$
31.6.a.b	$x^{8} - 5x^{7} - 1990x^{6} + 15987x^{5} + 1159441x^{4} - 9889532x^{3} - 211195384x^{2} + 1094532384x + 13261728528$

Dimensions

Newforms $S_{6}^{\mathrm{new}}(\Gamma_0(31))$	13
Old forms	0
Cusp forms $S_{6}(\Gamma_0(31))$	13
Eisenstein series $E_{6}(\Gamma_0(31))$	2
Modular forms $M_{6}(\Gamma_0(31))$	15

Decomposition of the old subspace

The old subspace is 0.

Provenance

Stored in the atlas: computed by Sagebrush's modular symbols engine in 0.217 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, 31]: [1, 15] (certified at ell = 2147482951)
T = [(2, 1), (3, 1)]; h of degree 13 = 1 x 13 (phi(ord eps) x dim S_k^new); 3 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(31, 6)

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

cargo run --release -p sagebrush-web --example atlas -- 31:6 1000

← 30.6.a · 32.6.a →