Atlas › Modular forms › Weight 2 › Level 184 › 184.2.a

Newspace 184.2.a: $S_{2}^{\mathrm{new}}(\Gamma_0(184))$

Newforms

Label	Dim	Coefficient field	Trace form	AL signs	Elliptic curve
184.2.a.a	1	$\mathbb{Q}$	$q - q^{3} - 4q^{5} + 2q^{7} + O(q^{8})$	−	184a1 rank 1
184.2.a.b	1	$\mathbb{Q}$	$q - q^{3} - 2q^{5} - 4q^{7} + O(q^{8})$	+	184b1 rank 1
184.2.a.c	1	$\mathbb{Q}$	$q + 4q^{7} + O(q^{8})$	−	184c1 rank 0
184.2.a.d	1	$\mathbb{Q}$	$q + 3q^{3} - 2q^{7} + O(q^{8})$	−	184d1 rank 0
184.2.a.e	2	$\mathbb{Q}(\sqrt{17})$	$2q - q^{3} + 4q^{5} + O(q^{8})$	+

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 $T$
184.2.a.a	$x + 13$
184.2.a.b	$x + 7$
184.2.a.c	$x$
184.2.a.d	$x - 3$
184.2.a.e	$x^{2} - 11x + 26$

Dimensions

Newforms $S_{2}^{\mathrm{new}}(\Gamma_0(184))$	6
Old forms	15
Cusp forms $S_{2}(\Gamma_0(184))$	21
Eisenstein series $E_{2}(\Gamma_0(184))$	7
Modular forms $M_{2}(\Gamma_0(184))$	28

Decomposition of the old subspace

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

Provenance

Stored in the atlas: computed by Sagebrush's modular symbols engine in 0.319 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]: [0, 1, 2, 3, 3, 8, 15, 28] (certified at ell = 2147483647)
T = [(3, 1), (5, 3)]; h of degree 6 = 1 x 6 (phi(ord eps) x dim S_k^new); 1 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, 2)

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

cargo run --release -p sagebrush-web --example atlas -- 184:2 1000

← 183.2.a · 185.2.a →