Atlas › Modular forms › Weight 8 › Level 17 › 17.8.a

Newspace 17.8.a: $S_{8}^{\mathrm{new}}(\Gamma_0(17))$

Newforms

Label	Dim	Coefficient field	Trace form	AL signs	Sign
17.8.a.a	1	$\mathbb{Q}$	$q - 2q^{2} + 18q^{3} - 124q^{4} - 10q^{5} - 36q^{6} - 902q^{7} + O(q^{8})$	−	$-1$
17.8.a.b	3	degree 3	$3q + q^{2} - 86q^{3} + 225q^{4} - 198q^{5} - 1524q^{6} - 1558q^{7} + O(q^{8})$	−	$-1$
17.8.a.c	6	degree 6	$6q + 15q^{2} + 40q^{3} + 485q^{4} - 184q^{5} + 1882q^{6} + 2064q^{7} + O(q^{8})$	+	$+1$

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 $T$
17.8.a.a	$x - 16$
17.8.a.b	$x^{3} + 85x^{2} + 1002x + 3196$
17.8.a.c	$x^{6} - 55x^{5} - 10480x^{4} + 594968x^{3} + 21446476x^{2} - 1401799020x + 10072288656$

Dimensions

Newforms $S_{8}^{\mathrm{new}}(\Gamma_0(17))$	10
Old forms	0
Cusp forms $S_{8}(\Gamma_0(17))$	10
Eisenstein series $E_{8}(\Gamma_0(17))$	2
Modular forms $M_{8}(\Gamma_0(17))$	12

Decomposition of the old subspace

The old subspace is 0.

Provenance

Stored in the atlas: computed by Sagebrush's modular symbols engine in 0.257 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, 12] (certified at ell = 2147483489)
T = [(2, 1), (3, 1)]; h of degree 10 = 1 x 10 (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(17, 8)

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

cargo run --release -p sagebrush-web --example atlas -- 17:8 1000

← 16.8.a · 18.8.a →