Atlas › Modular forms › Weight 2 › Level 181 › 181.2.a

Newspace 181.2.a: $S_{2}^{\mathrm{new}}(\Gamma_0(181))$

Newforms

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

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 $T$
181.2.a.a	$x^{5} + 8x^{4} + 21x^{3} + 20x^{2} + 4x - 1$
181.2.a.b	$x^{9} - 6x^{8} - 15x^{7} + 136x^{6} - 75x^{5} - 641x^{4} + 775x^{3} + 578x^{2} - 862x + 73$

Dimensions

Newforms $S_{2}^{\mathrm{new}}(\Gamma_0(181))$	14
Old forms	0
Cusp forms $S_{2}(\Gamma_0(181))$	14
Eisenstein series $E_{2}(\Gamma_0(181))$	1
Modular forms $M_{2}(\Gamma_0(181))$	15

Decomposition of the old subspace

The old subspace is 0.

Provenance

Stored in the atlas: computed by Sagebrush's modular symbols engine in 0.161 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, 181]: [0, 15] (certified at ell = 2147482801)
T = [(2, 1), (3, 1)]; 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(181, 2)

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

cargo run --release -p sagebrush-web --example atlas -- 181:2 1000

← 180.2.a · 182.2.a →