Atlas › Modular forms › Weight 10 › Level 29 › 29.10.a

Newspace 29.10.a: $S_{10}^{\mathrm{new}}(\Gamma_0(29))$

Newforms

Label	Dim	Coefficient field	Trace form	AL signs	Sign	CM	Elliptic curve
29.10.a.a	9	degree 9	$9q - 244q^{3} + 1194q^{4} - 738q^{5} - 2330q^{6} - 7128q^{7} + O(q^{8})$	+	$-1$
29.10.a.b	12	degree 12	$12q + 16q^{2} + 242q^{3} + 3498q^{4} + 1762q^{5} + 5446q^{6} + 12080q^{7} + O(q^{8})$	−	$+1$

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 $T$
29.10.a.a	$x^{9} + 244x^{8} - 75885x^{7} - 15893670x^{6} + 2188254679x^{5} + 298460397160x^{4} - 24455930684547x^{3} - 1131583192745078x^{2} + 4771480185165784x + 43851759845977856$
29.10.a.b	$x^{12} - 258x^{11} - 116596x^{10} + 27201108x^{9} + 5306688394x^{8} - 998994873488x^{7} - 123013940482576x^{6} + 15800217471906180x^{5} + 1514193085561310445x^{4} - 99305259061604545550x^{3} - 8618670563607879603300x^{2} + 127588494093131623077000x + 11170825094960211961980000$

Dimensions

Newforms $S_{10}^{\mathrm{new}}(\Gamma_0(29))$	21
Old forms	0
Cusp forms $S_{10}(\Gamma_0(29))$	21
Eisenstein series $E_{10}(\Gamma_0(29))$	2
Modular forms $M_{10}(\Gamma_0(29))$	23

Decomposition of the old subspace

The old subspace is 0.

Provenance

Stored in the atlas: computed by Sagebrush's modular symbols engine in 0.308 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, 23] (certified at ell = 2147483549)
T = [(2, 1), (3, 1)]; h of degree 21 = 1 x 21 (phi(ord eps) x dim S_k^new); 6 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, 10)

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

cargo run --release -p sagebrush-web --example atlas -- 29:10 1000

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