Atlas › Modular forms › Weight 6 › Level 29 › 29.6.a

Newspace 29.6.a: $S_{6}^{\mathrm{new}}(\Gamma_0(29))$

Newforms

Label	Dim	Coefficient field	Trace form	AL signs	Sign	CM	Elliptic curve
29.6.a.a	4	degree 4	$4q - 28q^{3} + 10q^{4} - 68q^{5} - 194q^{6} - 208q^{7} + O(q^{8})$	+	$-1$
29.6.a.b	7	degree 7	$7q + 4q^{2} + 26q^{3} + 154q^{4} + 32q^{5} + 22q^{6} + 184q^{7} + O(q^{8})$	−	$+1$

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 $T$
29.6.a.a	$x^{4} + 28x^{3} + 171x^{2} - 980x - 8704$
29.6.a.b	$x^{7} - 30x^{6} - 1114x^{5} + 39408x^{4} + 116505x^{3} - 9632930x^{2} + 22233300x + 350796600$

Dimensions

Newforms $S_{6}^{\mathrm{new}}(\Gamma_0(29))$	11
Old forms	0
Cusp forms $S_{6}(\Gamma_0(29))$	11
Eisenstein series $E_{6}(\Gamma_0(29))$	2
Modular forms $M_{6}(\Gamma_0(29))$	13

Decomposition of the old subspace

The old subspace is 0.

Provenance

Stored in the atlas: computed by Sagebrush's modular symbols engine in 0.214 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, 13] (certified at ell = 2147483549)
T = [(2, 1), (3, 1)]; h of degree 11 = 1 x 11 (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(29, 6)

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

cargo run --release -p sagebrush-web --example atlas -- 29:6 1000

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