Atlas › Modular forms › Weight 2 › Level 467 › 467.2.a

Newspace 467.2.a: $S_{2}^{\mathrm{new}}(\Gamma_0(467))$

Newforms

Label	Dim	Coefficient field	Trace form	AL signs	Sign	Elliptic curve
467.2.a.a	1	$\mathbb{Q}$	$q - 3q^{3} - 2q^{4} + 2q^{5} + q^{7} + O(q^{8})$	+	$-1$	467a1 rank 1
467.2.a.b	12	degree 12	$12q - 5q^{2} - 3q^{3} + 7q^{4} - 7q^{5} - 3q^{6} - 12q^{7} + O(q^{8})$	+	$-1$
467.2.a.c	26	degree 26	$26q + 5q^{2} + 4q^{3} + 33q^{4} + 3q^{5} - 3q^{6} + 11q^{7} + O(q^{8})$	−	$+1$

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 $T$
467.2.a.a	$x + 3$
467.2.a.b	$x^{12} + 8x^{11} + 4x^{10} - 82x^{9} - 83x^{8} + 315x^{7} + 183x^{6} - 549x^{5} + 88x^{4} + 159x^{3} - 41x^{2} - 3x + 1$
467.2.a.c	$x^{26} - 9x^{25} - 53x^{24} + 649x^{23} + 814x^{22} - 19447x^{21} + 3358x^{20} + 319374x^{19} - 240958x^{18} - 3208940x^{17} + 3035847x^{16} + 20867128x^{15} - 18433838x^{14} - 89962822x^{13} + 56243433x^{12} + 254111628x^{11} - 58544501x^{10} - 436261101x^{9} - 96791485x^{8} + 359299537x^{7} + 243818373x^{6} - 27636107x^{5} - 70591471x^{4} - 19580337x^{3} + 94825x^{2} + 517075x + 17021$

Dimensions

Newforms $S_{2}^{\mathrm{new}}(\Gamma_0(467))$	39
Old forms	0
Cusp forms $S_{2}(\Gamma_0(467))$	39
Eisenstein series $E_{2}(\Gamma_0(467))$	1
Modular forms $M_{2}(\Gamma_0(467))$	40

Decomposition of the old subspace

The old subspace is 0.

Provenance

Stored in the atlas: computed by Sagebrush's modular symbols engine in 0.193 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, 467]: [0, 40] (certified at ell = 2147483179)
T = [(2, 1), (3, 1)]; h of degree 39 = 1 x 39 (phi(ord eps) x dim S_k^new); 4 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(467, 2)

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

cargo run --release -p sagebrush-web --example atlas -- 467:2 1000

← 466.2.a · 468.2.a →