Atlas › Modular forms › Weight 2 › Level 673 › 673.2.a

Newspace 673.2.a: $S_{2}^{\mathrm{new}}(\Gamma_0(673))$

Newforms

Label	Dim	Coefficient field	Trace form	AL signs	Sign
673.2.a.a	2	$\mathbb{Q}(\sqrt{2})$	$2q + 2q^{2} - 2q^{4} + 4q^{7} + O(q^{8})$	−	$+1$
673.2.a.b	4	degree 4	$4q - q^{2} + 4q^{3} + 3q^{4} - 4q^{5} + 6q^{6} + 4q^{7} + O(q^{8})$	−	$+1$
673.2.a.c	24	degree 24	$24q + 3q^{2} + 9q^{3} + 31q^{4} + 20q^{5} - 4q^{6} + 7q^{7} + O(q^{8})$	−	$+1$
673.2.a.d	25	degree 25	$25q - 7q^{2} - 15q^{3} + 21q^{4} - 16q^{5} - 6q^{6} - 21q^{7} + O(q^{8})$	+	$-1$

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 $T$
673.2.a.a	$x^{2} - 2x - 7$
673.2.a.b	$x^{4} - 3x^{3} - 17x^{2} + 35x + 49$
673.2.a.c	$x^{24} - 12x^{23} - 8x^{22} + 610x^{21} - 1596x^{20} - 9935x^{19} + 45490x^{18} + 49439x^{17} - 489840x^{16} + 200145x^{15} + 2472679x^{14} - 2818419x^{13} - 5827910x^{12} + 9799744x^{11} + 5497673x^{10} - 13784295x^{9} - 959315x^{8} + 7931136x^{7} - 940885x^{6} - 1522842x^{5} + 242098x^{4} + 53321x^{3} + 380x^{2} - 160x - 3$
673.2.a.d	$x^{25} + 22x^{24} + 166x^{23} + 252x^{22} - 3053x^{21} - 14680x^{20} + 4956x^{19} + 167307x^{18} + 230007x^{17} - 813713x^{16} - 2130938x^{15} + 1492036x^{14} + 8440018x^{13} + 1691295x^{12} - 16903366x^{11} - 11399312x^{10} + 15948574x^{9} + 16676927x^{8} - 4882401x^{7} - 8782975x^{6} - 255401x^{5} + 1813831x^{4} + 263557x^{3} - 126396x^{2} - 21752x + 1273$

Dimensions

Newforms $S_{2}^{\mathrm{new}}(\Gamma_0(673))$	55
Old forms	0
Cusp forms $S_{2}(\Gamma_0(673))$	55
Eisenstein series $E_{2}(\Gamma_0(673))$	1
Modular forms $M_{2}(\Gamma_0(673))$	56

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, 673]: [0, 56] (certified at ell = 2147480161)
T = [(2, 1), (3, 1)]; h of degree 55 = 1 x 55 (phi(ord eps) x dim S_k^new); 6 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(673, 2)

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

cargo run --release -p sagebrush-web --example atlas -- 673:2 1000

← 672.2.a · 674.2.a →