Atlas › Modular forms › Weight 2 › Level 229 › 229.2.a

Newspace 229.2.a: $S_{2}^{\mathrm{new}}(\Gamma_0(229))$

Newforms

Label	Dim	Coefficient field	Trace form	AL signs	Sign	Elliptic curve
229.2.a.a	1	$\mathbb{Q}$	$q - q^{2} + q^{3} - q^{4} - 3q^{5} - q^{6} + 2q^{7} + O(q^{8})$	+	$-1$	229a1 rank 1
229.2.a.b	6	degree 6	$6q - 4q^{2} - 6q^{3} + 4q^{4} - 3q^{5} - q^{6} - 5q^{7} + O(q^{8})$	+	$-1$
229.2.a.c	11	degree 11	$11q + 5q^{2} + 3q^{3} + 11q^{4} + q^{7} + O(q^{8})$	−	$+1$

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 $T$
229.2.a.a	$x$
229.2.a.b	$x^{6} + 10x^{5} + 32x^{4} + 35x^{3} - 15x - 4$
229.2.a.c	$x^{11} - 8x^{10} - 8x^{9} + 201x^{8} - 297x^{7} - 1275x^{6} + 3286x^{5} + 1001x^{4} - 7152x^{3} + 1967x^{2} + 3270x + 50$

Dimensions

Newforms $S_{2}^{\mathrm{new}}(\Gamma_0(229))$	18
Old forms	0
Cusp forms $S_{2}(\Gamma_0(229))$	18
Eisenstein series $E_{2}(\Gamma_0(229))$	1
Modular forms $M_{2}(\Gamma_0(229))$	19

Decomposition of the old subspace

The old subspace is 0.

Provenance

Stored in the atlas: computed by Sagebrush's modular symbols engine in 0.252 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, 229]: [0, 19] (certified at ell = 2147478649)
T = [(2, 1), (3, 1)]; h of degree 18 = 1 x 18 (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(229, 2)

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

cargo run --release -p sagebrush-web --example atlas -- 229:2 1000

← 228.2.a · 230.2.a →