Atlas › Modular forms › Weight 2 › Level 283 › 283.2.a

Newspace 283.2.a: $S_{2}^{\mathrm{new}}(\Gamma_0(283))$

Newforms

Label	Dim	Coefficient field	Trace form	AL signs	Sign	CM	Elliptic curve
283.2.a.a	9	degree 9	$9q - 6q^{2} - 6q^{3} + 8q^{4} - 14q^{5} + 2q^{6} - 2q^{7} + O(q^{8})$	+	$-1$
283.2.a.b	14	degree 14	$14q + 6q^{2} + 4q^{3} + 16q^{4} + 14q^{5} - 2q^{6} + O(q^{8})$	−	$+1$

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 $T$
283.2.a.a	$x^{9} + 12x^{8} + 44x^{7} + 29x^{6} - 119x^{5} - 209x^{4} - 78x^{3} + 29x^{2} + 14x - 1$
283.2.a.b	$x^{14} - 10x^{13} + x^{12} + 273x^{11} - 641x^{10} - 2202x^{9} + 8767x^{8} + 2226x^{7} - 39214x^{6} + 31066x^{5} + 47094x^{4} - 66957x^{3} + 3026x^{2} + 25656x - 8968$

Dimensions

Newforms $S_{2}^{\mathrm{new}}(\Gamma_0(283))$	23
Old forms	0
Cusp forms $S_{2}(\Gamma_0(283))$	23
Eisenstein series $E_{2}(\Gamma_0(283))$	1
Modular forms $M_{2}(\Gamma_0(283))$	24

Decomposition of the old subspace

The old subspace is 0.

Provenance

Stored in the atlas: computed by Sagebrush's modular symbols engine in 0.168 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, 283]: [0, 24] (certified at ell = 2147480197)
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(283, 2)

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

cargo run --release -p sagebrush-web --example atlas -- 283:2 1000

← 282.2.a · 284.2.a →