Atlas › Modular forms › Weight 10 › Level 19 › 19.10.a

Newspace 19.10.a: $S_{10}^{\mathrm{new}}(\Gamma_0(19))$

Newforms

Label	Dim	Coefficient field	Trace form	AL signs	Sign	CM	Elliptic curve
19.10.a.a	6	degree 6	$6q - 33q^{2} - 155q^{3} + 1365q^{4} - 3612q^{5} + 5581q^{6} + 4085q^{7} + O(q^{8})$	+	$-1$
19.10.a.b	8	degree 8	$8q + 15q^{2} + 7q^{3} + 2645q^{4} + 3894q^{5} - 9723q^{6} - 7133q^{7} + O(q^{8})$	−	$+1$

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 $T$
19.10.a.a	$x^{6} + 188x^{5} - 57989x^{4} - 10000148x^{3} + 459954260x^{2} + 92468760928x + 1678674266112$
19.10.a.b	$x^{8} - 22x^{7} - 123495x^{6} + 6750378x^{5} + 4471450734x^{4} - 329333903580x^{3} - 37184855974632x^{2} + 1827374957035920x + 64654738149362688$

Dimensions

Newforms $S_{10}^{\mathrm{new}}(\Gamma_0(19))$	14
Old forms	0
Cusp forms $S_{10}(\Gamma_0(19))$	14
Eisenstein series $E_{10}(\Gamma_0(19))$	2
Modular forms $M_{10}(\Gamma_0(19))$	16

Decomposition of the old subspace

The old subspace is 0.

Provenance

Stored in the atlas: computed by Sagebrush's modular symbols engine in 0.294 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, 19]: [1, 16] (certified at ell = 2147483647)
T = [(2, 1), (3, 1)]; h of degree 14 = 1 x 14 (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(19, 10)

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

cargo run --release -p sagebrush-web --example atlas -- 19:10 1000

← 18.10.a · 20.10.a →