Atlas › Modular forms › Weight 6 › Level 17 › 17.6.a

Newspace 17.6.a: $S_{6}^{\mathrm{new}}(\Gamma_0(17))$

Newforms

Label	Dim	Coefficient field	Trace form	AL signs	Sign
17.6.a.a	1	$\mathbb{Q}$	$q - 6q^{2} + 10q^{3} + 4q^{4} - 72q^{5} - 60q^{6} - 196q^{7} + O(q^{8})$	+	$-1$
17.6.a.b	1	$\mathbb{Q}$	$q + q^{2} - 18q^{3} - 31q^{4} - 16q^{5} - 18q^{6} + 28q^{7} + O(q^{8})$	+	$-1$
17.6.a.c	4	degree 4	$4q + 3q^{2} + 28q^{3} + 69q^{4} + 80q^{5} + 184q^{6} + 284q^{7} + O(q^{8})$	−	$+1$

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 $T$
17.6.a.a	$x - 4$
17.6.a.b	$x + 17$
17.6.a.c	$x^{4} - 31x^{3} - 322x^{2} + 12668x - 58616$

Dimensions

Newforms $S_{6}^{\mathrm{new}}(\Gamma_0(17))$	6
Old forms	0
Cusp forms $S_{6}(\Gamma_0(17))$	6
Eisenstein series $E_{6}(\Gamma_0(17))$	2
Modular forms $M_{6}(\Gamma_0(17))$	8

Decomposition of the old subspace

The old subspace is 0.

Provenance

Stored in the atlas: computed by Sagebrush's modular symbols engine in 0.209 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, 8] (certified at ell = 2147483489)
T = [(2, 1), (3, 1)]; h of degree 6 = 1 x 6 (phi(ord eps) x dim S_k^new); 2 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, 6)

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

cargo run --release -p sagebrush-web --example atlas -- 17:6 1000

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