Atlas › Modular forms › Weight 4 › Level 47 › 47.4.a

Newspace 47.4.a: $S_{4}^{\mathrm{new}}(\Gamma_0(47))$

Newforms

Label	Dim	Coefficient field	Trace form	AL signs	Sign	CM	Elliptic curve
47.4.a.a	3	degree 3	$3q - 5q^{2} - 5q^{3} + 5q^{4} - 6q^{5} - 8q^{6} - 45q^{7} + O(q^{8})$	−	$-1$
47.4.a.b	8	degree 8	$8q + 3q^{2} + 7q^{3} + 45q^{4} + 14q^{5} + 16q^{6} + 39q^{7} + O(q^{8})$	+	$+1$

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 $T$
47.4.a.a	$x^{3} + 10x^{2} + 24x - 3$
47.4.a.b	$x^{8} - 10x^{7} - 175x^{6} + 2193x^{5} + 3021x^{4} - 111350x^{3} + 383800x^{2} - 203499x - 228937$

Dimensions

Newforms $S_{4}^{\mathrm{new}}(\Gamma_0(47))$	11
Old forms	0
Cusp forms $S_{4}(\Gamma_0(47))$	11
Eisenstein series $E_{4}(\Gamma_0(47))$	2
Modular forms $M_{4}(\Gamma_0(47))$	13

Decomposition of the old subspace

The old subspace is 0.

Provenance

Stored in the atlas: computed by Sagebrush's modular symbols engine in 0.093 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, 47]: [1, 13] (certified at ell = 2147483137)
T = [(2, 1), (3, 1)]; h of degree 11 = 1 x 11 (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(47, 4)

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

cargo run --release -p sagebrush-web --example atlas -- 47:4 1000

← 46.4.a · 48.4.a →