Atlas › Modular forms › Weight 2 › Level 263 › 263.2.a

Newspace 263.2.a: $S_{2}^{\mathrm{new}}(\Gamma_0(263))$

Newforms

Label	Dim	Coefficient field	Trace form	AL signs	Sign	CM	Elliptic curve
263.2.a.a	5	degree 5	$5q - 2q^{2} - 5q^{3} - 3q^{5} + q^{6} - 5q^{7} + O(q^{8})$	+	$-1$
263.2.a.b	17	degree 17	$17q + q^{2} + 7q^{3} + 19q^{4} + 3q^{5} - 3q^{6} + 7q^{7} + O(q^{8})$	−	$+1$

Hecke characteristic polynomials

The eigenvalue of $T = T_{2} + T_{3}$ 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 $T$
263.2.a.a	$x^{5} + 7x^{4} + 11x^{3} + 2x^{2} - 3x - 1$
263.2.a.b	$x^{17} - 8x^{16} - 30x^{15} + 369x^{14} + 38x^{13} - 6440x^{12} + 7592x^{11} + 51788x^{10} - 101882x^{9} - 175819x^{8} + 514051x^{7} + 69056x^{6} - 914265x^{5} + 580216x^{4} - 18608x^{3} - 30312x^{2} - 2837x - 67$

Dimensions

Newforms $S_{2}^{\mathrm{new}}(\Gamma_0(263))$	22
Old forms	0
Cusp forms $S_{2}(\Gamma_0(263))$	22
Eisenstein series $E_{2}(\Gamma_0(263))$	1
Modular forms $M_{2}(\Gamma_0(263))$	23

Decomposition of the old subspace

The old subspace is 0.

Provenance

Stored in the atlas: computed by Sagebrush's modular symbols engine in 0.171 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, 263]: [0, 23] (certified at ell = 2147482739)
T = [(2, 1), (3, 1)]; h of degree 22 = 1 x 22 (phi(ord eps) x dim S_k^new); 3 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(263, 2)

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

cargo run --release -p sagebrush-web --example atlas -- 263:2 1000

← 262.2.a · 264.2.a →