Atlas › Modular forms › Weight 4 › Level 152 › 152.4.a

Newspace 152.4.a: $S_{4}^{\mathrm{new}}(\Gamma_0(152))$

Newforms

Label	Dim	Coefficient field	Trace form	AL signs
152.4.a.a	2	$\mathbb{Q}(\sqrt{57})$	$2q - q^{3} - 5q^{5} - 6q^{7} + O(q^{8})$	+
152.4.a.b	3	degree 3	$3q - 5q^{3} + 2q^{5} - 35q^{7} + O(q^{8})$	−
152.4.a.c	3	degree 3	$3q + 4q^{3} + 7q^{5} + 7q^{7} + O(q^{8})$	+
152.4.a.d	5	degree 5	$5q + 2q^{3} + 22q^{7} + O(q^{8})$	−

Hecke characteristic polynomials

The eigenvalue of $T = T_{3} + 3T_{5}$ 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 $T$
152.4.a.a	$x^{2} + 16x + 7$
152.4.a.b	$x^{3} - x^{2} - 1909x + 29197$
152.4.a.c	$x^{3} - 25x^{2} - 2521x + 41201$
152.4.a.d	$x^{5} - 2x^{4} - 6002x^{3} + 57088x^{2} + 7503241x - 130703078$

Dimensions

Newforms $S_{4}^{\mathrm{new}}(\Gamma_0(152))$	13
Old forms	43
Cusp forms $S_{4}(\Gamma_0(152))$	56
Eisenstein series $E_{4}(\Gamma_0(152))$	8
Modular forms $M_{4}(\Gamma_0(152))$	64

Decomposition of the old subspace

$S_{4}^{\mathrm{old}}(\Gamma_0(152)) =$ $S_{4}^{\mathrm{new}}(\Gamma_0(8))^{\oplus 2}$ $\oplus$ $S_{4}^{\mathrm{new}}(\Gamma_0(19))^{\oplus 4}$ $\oplus$ $S_{4}^{\mathrm{new}}(\Gamma_0(38))^{\oplus 3}$ $\oplus$ $S_{4}^{\mathrm{new}}(\Gamma_0(76))^{\oplus 2}$

Provenance

Stored in the atlas: computed by Sagebrush's modular symbols engine in 0.128 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, 2, 4, 8, 19, 38, 76, 152]: [1, 2, 3, 5, 6, 17, 33, 64] (certified at ell = 2147483647)
T = [(3, 1), (5, 3)]; h of degree 13 = 1 x 13 (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(152, 4)

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

cargo run --release -p sagebrush-web --example atlas -- 152:4 1000

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