Atlas › Modular forms › Weight 4 › Level 71 › 71.4.a

Newspace 71.4.a: $S_{4}^{\mathrm{new}}(\Gamma_0(71))$

Newforms

Label	Dim	Coefficient field	Trace form	AL signs	Sign
71.4.a.a	1	$\mathbb{Q}$	$q + q^{2} + q^{3} - 7q^{4} - 16q^{5} + q^{6} - q^{7} + O(q^{8})$	−	$-1$
71.4.a.b	4	degree 4	$4q - 3q^{2} - 6q^{3} + 5q^{4} - 9q^{5} - 31q^{6} - 35q^{7} + O(q^{8})$	−	$-1$
71.4.a.c	12	degree 12	$12q + 2q^{2} + 7q^{3} + 54q^{4} + 15q^{5} + 42q^{6} + 48q^{7} + O(q^{8})$	+	$+1$

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 $T$
71.4.a.a	$x - 2$
71.4.a.b	$x^{4} + 9x^{3} - 111x - 118$
71.4.a.c	$x^{12} - 9x^{11} - 319x^{10} + 2865x^{9} + 35482x^{8} - 330282x^{7} - 1505375x^{6} + 16327235x^{5} + 10071436x^{4} - 294235416x^{3} + 479866824x^{2} + 216446256x - 523980576$

Dimensions

Newforms $S_{4}^{\mathrm{new}}(\Gamma_0(71))$	17
Old forms	0
Cusp forms $S_{4}(\Gamma_0(71))$	17
Eisenstein series $E_{4}(\Gamma_0(71))$	2
Modular forms $M_{4}(\Gamma_0(71))$	19

Decomposition of the old subspace

The old subspace is 0.

Provenance

Stored in the atlas: computed by Sagebrush's modular symbols engine in 0.096 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, 71]: [1, 19] (certified at ell = 2147483171)
T = [(2, 1), (3, 1)]; h of degree 17 = 1 x 17 (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(71, 4)

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

cargo run --release -p sagebrush-web --example atlas -- 71:4 1000

← 70.4.a · 72.4.a →