Atlas › Modular forms › Weight 2 › Level 244 › 244.2.a

Newspace 244.2.a: $S_{2}^{\mathrm{new}}(\Gamma_0(244))$

Newforms

Label	Dim	Coefficient field	Trace form	AL signs	Sign	CM	Elliptic curve
244.2.a.a	1	$\mathbb{Q}$	$q - 3q^{5} - 3q^{7} + O(q^{8})$	−			244a1 rank 1
244.2.a.b	4	degree 4	$4q + 5q^{5} - q^{7} + O(q^{8})$	+

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 $T$
244.2.a.a	$x + 3$
244.2.a.b	$x^{4} - 5x^{3} - 19x^{2} + 105x - 98$

Dimensions

Newforms $S_{2}^{\mathrm{new}}(\Gamma_0(244))$	5
Old forms	24
Cusp forms $S_{2}(\Gamma_0(244))$	29
Eisenstein series $E_{2}(\Gamma_0(244))$	5
Modular forms $M_{2}(\Gamma_0(244))$	34

Decomposition of the old subspace

$S_{2}^{\mathrm{old}}(\Gamma_0(244)) =$ $S_{2}^{\mathrm{new}}(\Gamma_0(61))^{\oplus 3}$ $\oplus$ $S_{2}^{\mathrm{new}}(\Gamma_0(122))^{\oplus 2}$

Provenance

Stored in the atlas: computed by Sagebrush's modular symbols engine in 0.178 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, 61, 122, 244]: [0, 1, 2, 5, 17, 34] (certified at ell = 2147482921)
T = [(3, 1), (5, 1)]; h of degree 5 = 1 x 5 (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(244, 2)

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

cargo run --release -p sagebrush-web --example atlas -- 244:2 1000

← 243.2.a · 245.2.a →