Atlas › Modular forms › Weight 2 › Level 124 › 124.2.a

Newspace 124.2.a: $S_{2}^{\mathrm{new}}(\Gamma_0(124))$

Newforms

Label	Dim	Coefficient field	Trace form	AL signs	Sign	CM	Elliptic curve
124.2.a.a	1	$\mathbb{Q}$	$q - 2q^{3} - 3q^{5} - q^{7} + O(q^{8})$	−			124a1 rank 1
124.2.a.b	1	$\mathbb{Q}$	$q + q^{5} + 3q^{7} + O(q^{8})$	+			124b1 rank 0

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 $T$
124.2.a.a	$x + 5$
124.2.a.b	$x - 1$

Dimensions

Newforms $S_{2}^{\mathrm{new}}(\Gamma_0(124))$	2
Old forms	12
Cusp forms $S_{2}(\Gamma_0(124))$	14
Eisenstein series $E_{2}(\Gamma_0(124))$	5
Modular forms $M_{2}(\Gamma_0(124))$	19

Decomposition of the old subspace

$S_{2}^{\mathrm{old}}(\Gamma_0(124)) =$ $S_{2}^{\mathrm{new}}(\Gamma_0(31))^{\oplus 3}$ $\oplus$ $S_{2}^{\mathrm{new}}(\Gamma_0(62))^{\oplus 2}$

Provenance

Stored in the atlas: computed by Sagebrush's modular symbols engine in 0.194 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, 31, 62, 124]: [0, 1, 2, 3, 10, 19] (certified at ell = 2147482951)
T = [(3, 1), (5, 1)]; h of degree 2 = 1 x 2 (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(124, 2)

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

cargo run --release -p sagebrush-web --example atlas -- 124:2 1000

← 123.2.a · 125.2.a →