Atlas › Modular forms › Weight 2 › Level 167 › 167.2.a

Newspace 167.2.a: $S_{2}^{\mathrm{new}}(\Gamma_0(167))$

Newforms

Label	Dim	Coefficient field	Trace form	AL signs	Sign	CM	Elliptic curve
167.2.a.a	2	$\mathbb{Q}(\sqrt{5})$	$2q - q^{2} - q^{3} - q^{4} - 2q^{5} - 2q^{6} - 5q^{7} + O(q^{8})$	+	$-1$
167.2.a.b	12	degree 12	$12q + 2q^{2} + 3q^{3} + 14q^{4} + 4q^{5} - 6q^{6} + 11q^{7} + O(q^{8})$	−	$+1$

Hecke characteristic polynomials

The eigenvalue of $T = T_{2} + 3T_{3}$ 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 $T$
167.2.a.a	$x^{2} + 4x - 1$
167.2.a.b	$x^{12} - 11x^{11} - 179x^{10} + 2277x^{9} + 7507x^{8} - 143202x^{7} + 63800x^{6} + 2992752x^{5} - 5606187x^{4} - 13117270x^{3} + 24571265x^{2} + 17224374x - 7449939$

Dimensions

Newforms $S_{2}^{\mathrm{new}}(\Gamma_0(167))$	14
Old forms	0
Cusp forms $S_{2}(\Gamma_0(167))$	14
Eisenstein series $E_{2}(\Gamma_0(167))$	1
Modular forms $M_{2}(\Gamma_0(167))$	15

Decomposition of the old subspace

The old subspace is 0.

Provenance

Stored in the atlas: computed by Sagebrush's modular symbols engine in 0.164 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, 167]: [0, 15] (certified at ell = 2147483237)
T = [(2, 1), (3, 3)]; h of degree 14 = 1 x 14 (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(167, 2)

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

cargo run --release -p sagebrush-web --example atlas -- 167:2 1000

← 166.2.a · 168.2.a →