Atlas › Modular forms › Weight 4 › Level 29 › 29.4.a

Newspace 29.4.a: $S_{4}^{\mathrm{new}}(\Gamma_0(29))$

Newforms

Label	Dim	Coefficient field	Trace form	AL signs	Sign	CM	Elliptic curve
29.4.a.a	2	$\mathbb{Q}(\sqrt{2})$	$2q - 2q^{2} - 10q^{3} - 10q^{4} - 10q^{5} - 2q^{6} - 16q^{7} + O(q^{8})$	−	$-1$
29.4.a.b	5	degree 5	$5q + 8q^{3} + 26q^{4} + 10q^{5} + 34q^{6} + 40q^{7} + O(q^{8})$	+	$+1$

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 $T$
29.4.a.a	$x^{2} + 12x + 28$
29.4.a.b	$x^{5} - 8x^{4} - 119x^{3} + 1154x^{2} - 3096x + 2592$

Dimensions

Newforms $S_{4}^{\mathrm{new}}(\Gamma_0(29))$	7
Old forms	0
Cusp forms $S_{4}(\Gamma_0(29))$	7
Eisenstein series $E_{4}(\Gamma_0(29))$	2
Modular forms $M_{4}(\Gamma_0(29))$	9

Decomposition of the old subspace

The old subspace is 0.

Provenance

Stored in the atlas: computed by Sagebrush's modular symbols engine in 0.095 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, 29]: [1, 9] (certified at ell = 2147483549)
T = [(2, 1), (3, 1)]; h of degree 7 = 1 x 7 (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(29, 4)

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

cargo run --release -p sagebrush-web --example atlas -- 29:4 1000

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