Atlas › Modular forms › Weight 2 › Level 281 › 281.2.a

Newspace 281.2.a: $S_{2}^{\mathrm{new}}(\Gamma_0(281))$

Newforms

Label	Dim	Coefficient field	Trace form	AL signs	Sign	CM	Elliptic curve
281.2.a.a	7	degree 7	$7q - 2q^{2} - 4q^{3} - 4q^{5} - 5q^{6} - 12q^{7} + O(q^{8})$	+	$-1$
281.2.a.b	16	degree 16	$16q - q^{2} + 4q^{3} + 23q^{4} + 2q^{5} + 5q^{6} + 16q^{7} + O(q^{8})$	−	$+1$

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 $T$
281.2.a.a	$x^{7} + 6x^{6} + 6x^{5} - 17x^{4} - 20x^{3} + 20x^{2} + 12x - 9$
281.2.a.b	$x^{16} - 3x^{15} - 60x^{14} + 187x^{13} + 1308x^{12} - 4255x^{11} - 12774x^{10} + 44656x^{9} + 56761x^{8} - 236033x^{7} - 86178x^{6} + 623316x^{5} - 91746x^{4} - 741544x^{3} + 315940x^{2} + 313385x - 182959$

Dimensions

Newforms $S_{2}^{\mathrm{new}}(\Gamma_0(281))$	23
Old forms	0
Cusp forms $S_{2}(\Gamma_0(281))$	23
Eisenstein series $E_{2}(\Gamma_0(281))$	1
Modular forms $M_{2}(\Gamma_0(281))$	24

Decomposition of the old subspace

The old subspace is 0.

Provenance

Stored in the atlas: computed by Sagebrush's modular symbols engine in 0.17 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, 281]: [0, 24] (certified at ell = 2147482681)
T = [(2, 1), (3, 1)]; h of degree 23 = 1 x 23 (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(281, 2)

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

cargo run --release -p sagebrush-web --example atlas -- 281:2 1000

← 280.2.a · 282.2.a →