Atlas › Modular forms › Weight 2 › Level 292 › 292.2.a

Newspace 292.2.a: $S_{2}^{\mathrm{new}}(\Gamma_0(292))$

Newforms

Label	Dim	Coefficient field	Trace form	AL signs	Sign	CM	Elliptic curve
292.2.a.a	2	$\mathbb{Q}(\sqrt{5})$	$2q - q^{3} - 5q^{5} + O(q^{8})$	−
292.2.a.b	4	degree 4	$4q + 3q^{3} + 5q^{5} + O(q^{8})$	+

Hecke characteristic polynomials

The eigenvalue of $T = T_{3} + 3T_{5}$ 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 $T$
292.2.a.a	$x^{2} + 16x + 59$
292.2.a.b	$x^{4} - 18x^{3} + 49x^{2} + 124x - 236$

Dimensions

Newforms $S_{2}^{\mathrm{new}}(\Gamma_0(292))$	6
Old forms	29
Cusp forms $S_{2}(\Gamma_0(292))$	35
Eisenstein series $E_{2}(\Gamma_0(292))$	5
Modular forms $M_{2}(\Gamma_0(292))$	40

Decomposition of the old subspace

$S_{2}^{\mathrm{old}}(\Gamma_0(292)) =$ $S_{2}^{\mathrm{new}}(\Gamma_0(73))^{\oplus 3}$ $\oplus$ $S_{2}^{\mathrm{new}}(\Gamma_0(146))^{\oplus 2}$

Provenance

Stored in the atlas: computed by Sagebrush's modular symbols engine in 0.182 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, 2, 4, 73, 146, 292]: [0, 1, 2, 6, 20, 40] (certified at ell = 2147482873)
T = [(3, 1), (5, 3)]; h of degree 6 = 1 x 6 (phi(ord eps) x dim S_k^new); 1 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(292, 2)

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

cargo run --release -p sagebrush-web --example atlas -- 292:2 1000

← 291.2.a · 293.2.a →