Atlas › Modular forms › Weight 2 › Level 293 › 293.2.a

Newspace 293.2.a: $S_{2}^{\mathrm{new}}(\Gamma_0(293))$

Newforms

Label	Dim	Coefficient field	Trace form	AL signs	Sign	CM	Elliptic curve
293.2.a.a	8	degree 8	$8q - 3q^{2} - 8q^{3} + q^{4} - q^{5} + q^{6} - 13q^{7} + O(q^{8})$	+	$-1$
293.2.a.b	16	degree 16	$16q + 3q^{2} + 10q^{3} + 21q^{4} + q^{5} - q^{6} + 15q^{7} + O(q^{8})$	−	$+1$

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 $T$
293.2.a.a	$x^{8} + 11x^{7} + 36x^{6} + 18x^{5} - 78x^{4} - 93x^{3} + 3x^{2} + 40x + 13$
293.2.a.b	$x^{16} - 13x^{15} + 25x^{14} + 333x^{13} - 1506x^{12} - 1763x^{11} + 19186x^{10} - 11752x^{9} - 95072x^{8} + 121316x^{7} + 204263x^{6} - 325649x^{5} - 209259x^{4} + 335174x^{3} + 109821x^{2} - 111476x - 20716$

Dimensions

Newforms $S_{2}^{\mathrm{new}}(\Gamma_0(293))$	24
Old forms	0
Cusp forms $S_{2}(\Gamma_0(293))$	24
Eisenstein series $E_{2}(\Gamma_0(293))$	1
Modular forms $M_{2}(\Gamma_0(293))$	25

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, 293]: [0, 25] (certified at ell = 2147478961)
T = [(2, 1), (3, 1)]; h of degree 24 = 1 x 24 (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(293, 2)

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

cargo run --release -p sagebrush-web --example atlas -- 293:2 1000

← 292.2.a · 294.2.a →