Atlas › Modular forms › Weight 4 › Level 19 › 19.4.a

Newspace 19.4.a: $S_{4}^{\mathrm{new}}(\Gamma_0(19))$

Newforms

Label	Dim	Coefficient field	Trace form	AL signs	Sign	CM	Elliptic curve
19.4.a.a	1	$\mathbb{Q}$	$q - 3q^{2} - 5q^{3} + q^{4} - 12q^{5} + 15q^{6} + 11q^{7} + O(q^{8})$	−	$-1$
19.4.a.b	3	degree 3	$3q + 3q^{2} + q^{3} + 21q^{4} + 14q^{5} - 65q^{6} - 35q^{7} + O(q^{8})$	+	$+1$

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 $T$
19.4.a.a	$x + 8$
19.4.a.b	$x^{3} - 4x^{2} - 14x + 48$

Dimensions

Newforms $S_{4}^{\mathrm{new}}(\Gamma_0(19))$	4
Old forms	0
Cusp forms $S_{4}(\Gamma_0(19))$	4
Eisenstein series $E_{4}(\Gamma_0(19))$	2
Modular forms $M_{4}(\Gamma_0(19))$	6

Decomposition of the old subspace

The old subspace is 0.

Provenance

Stored in the atlas: computed by Sagebrush's modular symbols engine in 0.091 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, 6] (certified at ell = 2147483647)
T = [(2, 1), (3, 1)]; h of degree 4 = 1 x 4 (phi(ord eps) x dim S_k^new); 1 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, 4)

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

cargo run --release -p sagebrush-web --example atlas -- 19:4 1000

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