Atlas › Modular forms › Weight 8 › Level 29 › 29.8.a

Newspace 29.8.a: $S_{8}^{\mathrm{new}}(\Gamma_0(29))$

Newforms

Label	Dim	Coefficient field	Trace form	AL signs	Sign	CM	Elliptic curve
29.8.a.a	7	degree 7	$7q - 8q^{2} - 82q^{3} + 346q^{4} - 320q^{5} - 938q^{6} - 1704q^{7} + O(q^{8})$	−	$-1$
29.8.a.b	10	degree 10	$10q + 80q^{3} + 922q^{4} + 180q^{5} + 358q^{6} + 1040q^{7} + O(q^{8})$	+	$+1$

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 $T$
29.8.a.a	$x^{7} + 90x^{6} - 5318x^{5} - 490252x^{4} + 4031709x^{3} + 603956346x^{2} + 8841811860x + 35942621512$
29.8.a.b	$x^{10} - 80x^{9} - 14687x^{8} + 1113860x^{7} + 71958463x^{6} - 5289793280x^{5} - 129086782781x^{4} + 9719420309660x^{3} + 49472203198620x^{2} - 5777530641977040x + 50106826279797696$

Dimensions

Newforms $S_{8}^{\mathrm{new}}(\Gamma_0(29))$	17
Old forms	0
Cusp forms $S_{8}(\Gamma_0(29))$	17
Eisenstein series $E_{8}(\Gamma_0(29))$	2
Modular forms $M_{8}(\Gamma_0(29))$	19

Decomposition of the old subspace

The old subspace is 0.

Provenance

Stored in the atlas: computed by Sagebrush's modular symbols engine in 0.264 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, 19] (certified at ell = 2147483549)
T = [(2, 1), (3, 1)]; h of degree 17 = 1 x 17 (phi(ord eps) x dim S_k^new); 4 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, 8)

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

cargo run --release -p sagebrush-web --example atlas -- 29:8 1000

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