Atlas › Modular forms › Weight 10 › Level 17 › 17.10.a

Newspace 17.10.a: $S_{10}^{\mathrm{new}}(\Gamma_0(17))$

Newforms

Label	Dim	Coefficient field	Trace form	AL signs	Sign	CM	Elliptic curve
17.10.a.a	5	degree 5	$5q - 33q^{2} - 236q^{3} + 853q^{4} + 1480q^{5} + 7578q^{6} - 13202q^{7} + O(q^{8})$	+	$-1$
17.10.a.b	7	degree 7	$7q - q^{2} + 88q^{3} + 2389q^{4} + 1362q^{5} - 11720q^{6} + 9388q^{7} + O(q^{8})$	−	$+1$

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 $T$
17.10.a.a	$x^{5} + 269x^{4} - 27802x^{3} - 6757522x^{2} - 351003836x - 5442576560$
17.10.a.b	$x^{7} - 87x^{6} - 97082x^{5} + 8639428x^{4} + 2573036208x^{3} - 199559273264x^{2} - 19853344053984x + 1414782466180416$

Dimensions

Newforms $S_{10}^{\mathrm{new}}(\Gamma_0(17))$	12
Old forms	0
Cusp forms $S_{10}(\Gamma_0(17))$	12
Eisenstein series $E_{10}(\Gamma_0(17))$	2
Modular forms $M_{10}(\Gamma_0(17))$	14

Decomposition of the old subspace

The old subspace is 0.

Provenance

Stored in the atlas: computed by Sagebrush's modular symbols engine in 0.29 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, 17]: [1, 14] (certified at ell = 2147483489)
T = [(2, 1), (3, 1)]; h of degree 12 = 1 x 12 (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(17, 10)

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

cargo run --release -p sagebrush-web --example atlas -- 17:10 1000

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