Atlas › Modular forms › Weight 2 › Level 932 › 932.2.a

Newspace 932.2.a: $S_{2}^{\mathrm{new}}(\Gamma_0(932))$

Newforms

Label	Dim	Coefficient field	Trace form	AL signs	Sign	CM	Elliptic curve
932.2.a.a	7	degree 7	$7q - 4q^{3} - 5q^{5} - q^{7} + O(q^{8})$	−
932.2.a.b	13	degree 13	$13q + 6q^{3} + 5q^{5} - q^{7} + O(q^{8})$	+

Hecke characteristic polynomials

The eigenvalue of $T = T_{3} + T_{5}$ 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 $T$
932.2.a.a	$x^{7} + 9x^{6} + 15x^{5} - 27x^{4} - 14x^{3} + 25x^{2} - 9x + 1$
932.2.a.b	$x^{13} - 11x^{12} - 19x^{11} + 537x^{10} - 685x^{9} - 8776x^{8} + 20302x^{7} + 55788x^{6} - 174450x^{5} - 88071x^{4} + 508501x^{3} - 191557x^{2} - 165902x - 17542$

Dimensions

Newforms $S_{2}^{\mathrm{new}}(\Gamma_0(932))$	20
Old forms	95
Cusp forms $S_{2}(\Gamma_0(932))$	115
Eisenstein series $E_{2}(\Gamma_0(932))$	5
Modular forms $M_{2}(\Gamma_0(932))$	120

Decomposition of the old subspace

$S_{2}^{\mathrm{old}}(\Gamma_0(932)) =$ $S_{2}^{\mathrm{new}}(\Gamma_0(233))^{\oplus 3}$ $\oplus$ $S_{2}^{\mathrm{new}}(\Gamma_0(466))^{\oplus 2}$

Provenance

Stored in the atlas: computed by Sagebrush's modular symbols engine in 0.248 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, 233, 466, 932]: [0, 1, 2, 20, 60, 120] (certified at ell = 2147482481)
T = [(3, 1), (5, 1)]; h of degree 20 = 1 x 20 (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(932, 2)

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

cargo run --release -p sagebrush-web --example atlas -- 932:2 1000

← 931.2.a · 933.2.a →