Atlas › Modular forms › Weight 4 › Level 184 › 184.4.a

Newspace 184.4.a: $S_{4}^{\mathrm{new}}(\Gamma_0(184))$

Newforms

Label	Dim	Coefficient field	Trace form	AL signs
184.4.a.a	1	$\mathbb{Q}$	$q - 4q^{3} + 22q^{5} + 8q^{7} + O(q^{8})$	−
184.4.a.b	1	$\mathbb{Q}$	$q + 8q^{3} - 4q^{5} - 4q^{7} + O(q^{8})$	+
184.4.a.c	3	degree 3	$3q - 3q^{3} + 2q^{5} - 28q^{7} + O(q^{8})$	−
184.4.a.d	3	degree 3	$3q + q^{3} + 16q^{5} + 18q^{7} + O(q^{8})$	+
184.4.a.e	4	degree 4	$4q + q^{3} - 20q^{5} - 10q^{7} + O(q^{8})$	+
184.4.a.f	4	degree 4	$4q + 5q^{3} - 2q^{5} - 32q^{7} + O(q^{8})$	−

Hecke characteristic polynomials

The eigenvalue of $T = T_{3} + T_{5}$ 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 $T$
184.4.a.a	$x - 18$
184.4.a.b	$x - 4$
184.4.a.c	$x^{3} + x^{2} - 101x + 163$
184.4.a.d	$x^{3} - 17x^{2} - 549x + 7981$
184.4.a.e	$x^{4} + 19x^{3} + 39x^{2} - 615x - 828$
184.4.a.f	$x^{4} - 3x^{3} - 649x^{2} - 1481x + 46740$

Dimensions

Newforms $S_{4}^{\mathrm{new}}(\Gamma_0(184))$	16
Old forms	52
Cusp forms $S_{4}(\Gamma_0(184))$	68
Eisenstein series $E_{4}(\Gamma_0(184))$	8
Modular forms $M_{4}(\Gamma_0(184))$	76

Decomposition of the old subspace

$S_{4}^{\mathrm{old}}(\Gamma_0(184)) =$ $S_{4}^{\mathrm{new}}(\Gamma_0(8))^{\oplus 2}$ $\oplus$ $S_{4}^{\mathrm{new}}(\Gamma_0(23))^{\oplus 4}$ $\oplus$ $S_{4}^{\mathrm{new}}(\Gamma_0(46))^{\oplus 3}$ $\oplus$ $S_{4}^{\mathrm{new}}(\Gamma_0(92))^{\oplus 2}$

Provenance

Stored in the atlas: computed by Sagebrush's modular symbols engine in 0.134 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, 23, 46, 92, 184]: [1, 2, 3, 5, 7, 20, 39, 76] (certified at ell = 2147483647)
T = [(3, 1), (5, 1)]; h of degree 16 = 1 x 16 (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(184, 4)

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

cargo run --release -p sagebrush-web --example atlas -- 184:4 1000

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