Atlas › Modular forms › Weight 2 › Level 241 › 241.2.a

Newspace 241.2.a: $S_{2}^{\mathrm{new}}(\Gamma_0(241))$

Newforms

Label	Dim	Coefficient field	Trace form	AL signs	Sign	CM	Elliptic curve
241.2.a.a	7	degree 7	$7q - 4q^{2} - 3q^{3} + 2q^{4} - 8q^{5} - 5q^{6} - 7q^{7} + O(q^{8})$	+	$-1$
241.2.a.b	12	degree 12	$12q + 3q^{2} + q^{3} + 13q^{4} + 6q^{5} - q^{6} + 3q^{7} + O(q^{8})$	−	$+1$

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 $T$
241.2.a.a	$x^{7} + 7x^{6} + 12x^{5} - 9x^{4} - 40x^{3} - 33x^{2} - 10x - 1$
241.2.a.b	$x^{12} - 4x^{11} - 35x^{10} + 151x^{9} + 362x^{8} - 1959x^{7} - 458x^{6} + 9510x^{5} - 8056x^{4} - 9303x^{3} + 15123x^{2} - 6111x + 691$

Dimensions

Newforms $S_{2}^{\mathrm{new}}(\Gamma_0(241))$	19
Old forms	0
Cusp forms $S_{2}(\Gamma_0(241))$	19
Eisenstein series $E_{2}(\Gamma_0(241))$	1
Modular forms $M_{2}(\Gamma_0(241))$	20

Decomposition of the old subspace

The old subspace is 0.

Provenance

Stored in the atlas: computed by Sagebrush's modular symbols engine in 0.167 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, 241]: [0, 20] (certified at ell = 2147482801)
T = [(2, 1), (3, 1)]; h of degree 19 = 1 x 19 (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(241, 2)

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

cargo run --release -p sagebrush-web --example atlas -- 241:2 1000

← 240.2.a · 242.2.a →