Atlas › Modular forms › Weight 2 › Level 183 › 183.2.a

Newspace 183.2.a: $S_{2}^{\mathrm{new}}(\Gamma_0(183))$

Newforms

Label	Dim	Coefficient field	Trace form	AL signs	Sign
183.2.a.a	2	$\mathbb{Q}(\sqrt{2})$	$2q - 2q^{2} - 2q^{3} + 2q^{4} - 2q^{5} + 2q^{6} - 2q^{7} + O(q^{8})$	+ +	$-1$
183.2.a.b	3	degree 3	$3q + q^{2} - 3q^{3} + q^{4} + 6q^{5} - q^{6} + O(q^{8})$	+ −	$+1$
183.2.a.c	6	degree 6	$6q + 6q^{3} + 10q^{4} + 2q^{5} + 2q^{7} + O(q^{8})$	− +	$+1$

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 $T$
183.2.a.a	$x^{2} + 4x + 2$
183.2.a.b	$x^{3} - 7x^{2} + 13x - 5$
183.2.a.c	$x^{6} - 2x^{5} - 28x^{4} + 44x^{3} - 15x^{2} - 4x + 2$

Dimensions

Newforms $S_{2}^{\mathrm{new}}(\Gamma_0(183))$	11
Old forms	8
Cusp forms $S_{2}(\Gamma_0(183))$	19
Eisenstein series $E_{2}(\Gamma_0(183))$	3
Modular forms $M_{2}(\Gamma_0(183))$	22

Decomposition of the old subspace

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

Provenance

Stored in the atlas: computed by Sagebrush's modular symbols engine in 0.174 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]: [0, 1, 5, 22] (certified at ell = 2147482921)
T = [(2, 1), (5, 1)]; h of degree 11 = 1 x 11 (phi(ord eps) x dim S_k^new); 2 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, 2)

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

cargo run --release -p sagebrush-web --example atlas -- 183:2 1000

← 182.2.a · 184.2.a →