Atlas › Modular forms › Weight 12 › Level 1 › 1.12.a

Newspace 1.12.a: $S_{12}^{\mathrm{new}}(\Gamma_0(1))$

Newforms

Label	Dim	Coefficient field	Trace form	AL signs	Sign	CM	Elliptic curve
1.12.a.a	1	$\mathbb{Q}$	$q - 24q^{2} + 252q^{3} - 1472q^{4} + 4830q^{5} - 6048q^{6} - 16744q^{7} + O(q^{8})$		$+1$

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 $T$
1.12.a.a	$x - 228$

Dimensions

Newforms $S_{12}^{\mathrm{new}}(\Gamma_0(1))$	1
Old forms	0
Cusp forms $S_{12}(\Gamma_0(1))$	1
Eisenstein series $E_{12}(\Gamma_0(1))$	1
Modular forms $M_{12}(\Gamma_0(1))$	2

Decomposition of the old subspace

The old subspace is 0.

Provenance

Stored in the atlas: computed by Sagebrush's modular symbols engine in 0.247 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]: [2] (certified at ell = 2147483647)
T = [(2, 1), (3, 1)]; h of degree 1 = 1 x 1 (phi(ord eps) x dim S_k^new); 1 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(1, 12)

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

cargo run --release -p sagebrush-web --example atlas -- 1:12 1000

2.12.a →