Atlas › Modular forms › Weight 2 › Level 652 › 652.2.a

Newspace 652.2.a: $S_{2}^{\mathrm{new}}(\Gamma_0(652))$

Newforms

Label	Dim	Coefficient field	Trace form	AL signs
652.2.a.a	2	$\mathbb{Q}(\sqrt{2})$	$2q - 4q^{7} + O(q^{8})$	+
652.2.a.b	5	degree 5	$5q + 5q^{3} - q^{5} + 8q^{7} + O(q^{8})$	+
652.2.a.c	6	degree 6	$6q - 5q^{3} - q^{5} - 8q^{7} + O(q^{8})$	−

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 $T$
652.2.a.a	$x^{2} - 18$
652.2.a.b	$x^{5} - 4x^{4} - 15x^{3} + 54x^{2} + 36x - 79$
652.2.a.c	$x^{6} + 6x^{5} + 3x^{4} - 38x^{3} - 68x^{2} - 19x + 12$

Dimensions

Newforms $S_{2}^{\mathrm{new}}(\Gamma_0(652))$	13
Old forms	67
Cusp forms $S_{2}(\Gamma_0(652))$	80
Eisenstein series $E_{2}(\Gamma_0(652))$	5
Modular forms $M_{2}(\Gamma_0(652))$	85

Decomposition of the old subspace

$S_{2}^{\mathrm{old}}(\Gamma_0(652)) =$ $S_{2}^{\mathrm{new}}(\Gamma_0(163))^{\oplus 3}$ $\oplus$ $S_{2}^{\mathrm{new}}(\Gamma_0(326))^{\oplus 2}$

Provenance

Stored in the atlas: computed by Sagebrush's modular symbols engine in 0.212 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, 163, 326, 652]: [0, 1, 2, 14, 43, 85] (certified at ell = 2147483179)
T = [(3, 1), (5, 1)]; h of degree 13 = 1 x 13 (phi(ord eps) x dim S_k^new); 2 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(652, 2)

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

cargo run --release -p sagebrush-web --example atlas -- 652:2 1000

← 651.2.a · 653.2.a →