Atlas › Modular forms › Weight 2 › Level 276 › 276.2.a

Newspace 276.2.a: $S_{2}^{\mathrm{new}}(\Gamma_0(276))$

Newforms

Label	Dim	Coefficient field	Trace form	AL signs	Sign	CM	Elliptic curve
276.2.a.a	2	$\mathbb{Q}(\sqrt{10})$	$2q - 2q^{3} + 4q^{7} + O(q^{8})$	+ +
276.2.a.b	2	$\mathbb{Q}(\sqrt{2})$	$2q + 2q^{3} + 4q^{5} + O(q^{8})$	− −

Hecke characteristic polynomials

The eigenvalue of $T = T_{5} + 3T_{7}$ 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 $T$
276.2.a.a	$x^{2} - 12x - 4$
276.2.a.b	$x^{2} - 4x - 28$

Dimensions

Newforms $S_{2}^{\mathrm{new}}(\Gamma_0(276))$	4
Old forms	39
Cusp forms $S_{2}(\Gamma_0(276))$	43
Eisenstein series $E_{2}(\Gamma_0(276))$	11
Modular forms $M_{2}(\Gamma_0(276))$	54

Decomposition of the old subspace

$S_{2}^{\mathrm{old}}(\Gamma_0(276)) =$ $S_{2}^{\mathrm{new}}(\Gamma_0(23))^{\oplus 6}$ $\oplus$ $S_{2}^{\mathrm{new}}(\Gamma_0(46))^{\oplus 4}$ $\oplus$ $S_{2}^{\mathrm{new}}(\Gamma_0(69))^{\oplus 3}$ $\oplus$ $S_{2}^{\mathrm{new}}(\Gamma_0(92))^{\oplus 2}$ $\oplus$ $S_{2}^{\mathrm{new}}(\Gamma_0(138))^{\oplus 2}$

Provenance

Stored in the atlas: computed by Sagebrush's modular symbols engine in 0.114 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, 3, 4, 6, 12, 23, 46, 69, 92, 138, 276]: [0, 1, 1, 2, 3, 5, 3, 8, 10, 15, 28, 54] (certified at ell = 2147483647)
T = [(5, 1), (7, 3)]; h of degree 4 = 1 x 4 (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(276, 2)

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

cargo run --release -p sagebrush-web --example atlas -- 276:2 1000

← 275.2.a · 277.2.a →