Atlas › Modular forms › Weight 2 › Level 367 › 367.2.a

Newspace 367.2.a: $S_{2}^{\mathrm{new}}(\Gamma_0(367))$

Newforms

Label	Dim	Coefficient field	Trace form	AL signs	Sign	CM	Elliptic curve
367.2.a.a	11	degree 11	$11q - 8q^{2} - 6q^{3} + 10q^{4} - 8q^{5} + q^{6} - 7q^{7} + O(q^{8})$	+	$-1$
367.2.a.b	19	degree 19	$19q + 9q^{2} + 4q^{3} + 21q^{4} + 6q^{5} - q^{6} + q^{7} + O(q^{8})$	−	$+1$

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 $T$
367.2.a.a	$x^{11} + 14x^{10} + 66x^{9} + 93x^{8} - 156x^{7} - 528x^{6} - 181x^{5} + 579x^{4} + 355x^{3} - 247x^{2} - 118x + 55$
367.2.a.b	$x^{19} - 13x^{18} + 13x^{17} + 478x^{16} - 1726x^{15} - 5496x^{14} + 34461x^{13} + 7964x^{12} - 287077x^{11} + 258711x^{10} + 1059939x^{9} - 1728454x^{8} - 1288541x^{7} + 3626413x^{6} - 590259x^{5} - 1752368x^{4} + 426879x^{3} + 210706x^{2} - 55183x + 1159$

Dimensions

Newforms $S_{2}^{\mathrm{new}}(\Gamma_0(367))$	30
Old forms	0
Cusp forms $S_{2}(\Gamma_0(367))$	30
Eisenstein series $E_{2}(\Gamma_0(367))$	1
Modular forms $M_{2}(\Gamma_0(367))$	31

Decomposition of the old subspace

The old subspace is 0.

Provenance

Stored in the atlas: computed by Sagebrush's modular symbols engine in 0.18 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, 367]: [0, 31] (certified at ell = 2147479381)
T = [(2, 1), (3, 1)]; h of degree 30 = 1 x 30 (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(367, 2)

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

cargo run --release -p sagebrush-web --example atlas -- 367:2 1000

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