Atlas › Modular forms › Weight 4 › Level 153 › 153.4.a

Newspace 153.4.a: $S_{4}^{\mathrm{new}}(\Gamma_0(153))$

Newforms

Label	Dim	Coefficient field	Trace form	AL signs
153.4.a.a	1	$\mathbb{Q}$	$q - q^{2} - 7q^{4} + 10q^{5} - 8q^{7} + O(q^{8})$	+
153.4.a.b	1	$\mathbb{Q}$	$q + q^{2} - 7q^{4} - 16q^{5} + 34q^{7} + O(q^{8})$	−
153.4.a.c	1	$\mathbb{Q}$	$q + q^{2} - 7q^{4} + 20q^{5} - 2q^{7} + O(q^{8})$	−
153.4.a.d	1	$\mathbb{Q}$	$q + 3q^{2} + q^{4} - 6q^{5} - 28q^{7} + O(q^{8})$	+
153.4.a.e	2	$\mathbb{Q}(\sqrt{2})$	$2q + 20q^{4} - 6q^{5} - 8q^{7} + O(q^{8})$	−
153.4.a.f	3	degree 3	$3q - 5q^{2} + 13q^{4} - 8q^{5} - 8q^{7} + O(q^{8})$	+
153.4.a.g	3	degree 3	$3q - q^{2} + 25q^{4} + 8q^{5} + 22q^{7} + O(q^{8})$	−
153.4.a.h	4	degree 4	$4q - 4q^{2} + 26q^{4} - 22q^{5} - 24q^{7} + O(q^{8})$	−
153.4.a.i	4	degree 4	$4q + 4q^{2} + 26q^{4} + 22q^{5} - 24q^{7} + O(q^{8})$	+

Hecke characteristic polynomials

The eigenvalue of $T = T_{2} + T_{5}$ 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 $T$
153.4.a.a	$x - 9$
153.4.a.b	$x + 15$
153.4.a.c	$x - 21$
153.4.a.d	$x + 3$
153.4.a.e	$x^{2} + 6x - 441$
153.4.a.f	$x^{3} + 13x^{2} + 13x - 171$
153.4.a.g	$x^{3} - 7x^{2} - 20x + 132$
153.4.a.h	$x^{4} + 26x^{3} - 8x^{2} - 4254x - 25857$
153.4.a.i	$x^{4} - 26x^{3} - 8x^{2} + 4254x - 25857$

Dimensions

Newforms $S_{4}^{\mathrm{new}}(\Gamma_0(153))$	20
Old forms	30
Cusp forms $S_{4}(\Gamma_0(153))$	50
Eisenstein series $E_{4}(\Gamma_0(153))$	8
Modular forms $M_{4}(\Gamma_0(153))$	58

Decomposition of the old subspace

$S_{4}^{\mathrm{old}}(\Gamma_0(153)) =$ $S_{4}^{\mathrm{new}}(\Gamma_0(9))^{\oplus 2}$ $\oplus$ $S_{4}^{\mathrm{new}}(\Gamma_0(17))^{\oplus 3}$ $\oplus$ $S_{4}^{\mathrm{new}}(\Gamma_0(51))^{\oplus 2}$

Provenance

Stored in the atlas: computed by Sagebrush's modular symbols engine in 0.124 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, 3, 9, 17, 51, 153]: [1, 2, 4, 6, 20, 56] (certified at ell = 2147483137)
T = [(2, 1), (5, 1)]; h of degree 20 = 1 x 20 (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(153, 4)

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

cargo run --release -p sagebrush-web --example atlas -- 153:4 1000

← 152.4.a · 154.4.a →