Atlas › Modular forms › Weight 2 › Level 239 › 239.2.a

Newspace 239.2.a: $S_{2}^{\mathrm{new}}(\Gamma_0(239))$

Newforms

Label	Dim	Coefficient field	Trace form	AL signs	Sign	CM	Elliptic curve
239.2.a.a	3	degree 3	$3q - q^{2} - q^{3} - q^{4} - 4q^{5} - 2q^{6} - 3q^{7} + O(q^{8})$	+	$-1$
239.2.a.b	17	degree 17	$17q + 3q^{3} + 22q^{4} + 6q^{5} + 2q^{6} + 5q^{7} + O(q^{8})$	−	$+1$

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 $T$
239.2.a.a	$x^{3} + 2x^{2} - x - 1$
239.2.a.b	$x^{17} - 3x^{16} - 65x^{15} + 214x^{14} + 1557x^{13} - 5760x^{12} - 16571x^{11} + 73712x^{10} + 70240x^{9} - 469977x^{8} - 6891x^{7} + 1468432x^{6} - 659353x^{5} - 2067403x^{4} + 1258919x^{3} + 1183921x^{2} - 575531x - 241031$

Dimensions

Newforms $S_{2}^{\mathrm{new}}(\Gamma_0(239))$	20
Old forms	0
Cusp forms $S_{2}(\Gamma_0(239))$	20
Eisenstein series $E_{2}(\Gamma_0(239))$	1
Modular forms $M_{2}(\Gamma_0(239))$	21

Decomposition of the old subspace

The old subspace is 0.

Provenance

Stored in the atlas: computed by Sagebrush's modular symbols engine in 0.169 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, 239]: [0, 21] (certified at ell = 2147482093)
T = [(2, 1), (3, 1)]; h of degree 20 = 1 x 20 (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(239, 2)

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

cargo run --release -p sagebrush-web --example atlas -- 239:2 1000

← 238.2.a · 240.2.a →