Atlas › Modular forms › Weight 4 › Level 183 › 183.4.a

Newspace 183.4.a: $S_{4}^{\mathrm{new}}(\Gamma_0(183))$

Newforms

Label	Dim	Coefficient field	Trace form	AL signs	Sign
183.4.a.a	1	$\mathbb{Q}$	$q + q^{2} + 3q^{3} - 7q^{4} + 3q^{5} + 3q^{6} - 14q^{7} + O(q^{8})$	− +	$-1$
183.4.a.b	3	degree 3	$3q - 2q^{2} + 9q^{3} - 2q^{4} - 28q^{5} - 6q^{6} - 4q^{7} + O(q^{8})$	− +	$-1$
183.4.a.c	7	degree 7	$7q - 3q^{2} - 21q^{3} + 27q^{4} - 15q^{5} + 9q^{6} - 4q^{7} + O(q^{8})$	+ −	$-1$
183.4.a.d	8	degree 8	$8q + 3q^{2} - 24q^{3} + 23q^{4} + 25q^{5} - 9q^{6} + 10q^{7} + O(q^{8})$	+ +	$+1$
183.4.a.e	11	degree 11	$11q + 5q^{2} + 33q^{3} + 59q^{4} + 15q^{5} + 15q^{6} + 52q^{7} + O(q^{8})$	− −	$+1$

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 $T$
183.4.a.a	$x - 4$
183.4.a.b	$x^{3} + 30x^{2} + 274x + 692$
183.4.a.c	$x^{7} + 18x^{6} - 275x^{5} - 4212x^{4} + 24172x^{3} + 212280x^{2} - 457216x + 56160$
183.4.a.d	$x^{8} - 28x^{7} - 416x^{6} + 13952x^{5} + 26677x^{4} - 1614054x^{3} + 1486850x^{2} + 2455628x + 457936$
183.4.a.e	$x^{11} - 20x^{10} - 997x^{9} + 24378x^{8} + 218825x^{7} - 7875942x^{6} - 3062649x^{5} + 954793624x^{4} - 2177864476x^{3} - 42930143624x^{2} + 95305316736x + 628479259296$

Dimensions

Newforms $S_{4}^{\mathrm{new}}(\Gamma_0(183))$	30
Old forms	30
Cusp forms $S_{4}(\Gamma_0(183))$	60
Eisenstein series $E_{4}(\Gamma_0(183))$	4
Modular forms $M_{4}(\Gamma_0(183))$	64

Decomposition of the old subspace

$S_{4}^{\mathrm{old}}(\Gamma_0(183)) =$ $S_{4}^{\mathrm{new}}(\Gamma_0(61))^{\oplus 2}$

Provenance

Stored in the atlas: computed by Sagebrush's modular symbols engine in 0.129 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, 61, 183]: [1, 2, 17, 64] (certified at ell = 2147482921)
T = [(2, 1), (5, 1)]; h of degree 30 = 1 x 30 (phi(ord eps) x dim S_k^new); 5 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(183, 4)

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

cargo run --release -p sagebrush-web --example atlas -- 183:4 1000

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