Atlas › Modular forms › Weight 2 › Level 271 › 271.2.a

Newspace 271.2.a: $S_{2}^{\mathrm{new}}(\Gamma_0(271))$

Newforms

Label	Dim	Coefficient field	Trace form	AL signs	Sign	CM	Elliptic curve
271.2.a.a	6	degree 6	$6q - 4q^{2} - q^{3} + 2q^{4} - 8q^{5} - 2q^{6} - 3q^{7} + O(q^{8})$	+	$-1$
271.2.a.b	16	degree 16	$16q + 5q^{2} + q^{3} + 17q^{4} + 10q^{5} - 4q^{6} - 3q^{7} + O(q^{8})$	−	$+1$

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 $T$
271.2.a.a	$x^{6} + 5x^{5} + 2x^{4} - 10x^{3} - 4x^{2} + 4x + 1$
271.2.a.b	$x^{16} - 6x^{15} - 44x^{14} + 322x^{13} + 488x^{12} - 6008x^{11} + 1457x^{10} + 48747x^{9} - 48149x^{8} - 184577x^{7} + 260329x^{6} + 303900x^{5} - 543667x^{4} - 152811x^{3} + 409517x^{2} + 12955x - 102211$

Dimensions

Newforms $S_{2}^{\mathrm{new}}(\Gamma_0(271))$	22
Old forms	0
Cusp forms $S_{2}(\Gamma_0(271))$	22
Eisenstein series $E_{2}(\Gamma_0(271))$	1
Modular forms $M_{2}(\Gamma_0(271))$	23

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, 271]: [0, 23] (certified at ell = 2147482801)
T = [(2, 1), (3, 1)]; h of degree 22 = 1 x 22 (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(271, 2)

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

cargo run --release -p sagebrush-web --example atlas -- 271:2 1000

← 270.2.a · 272.2.a →