Atlas › Modular forms › Weight 2 › Level 463 › 463.2.a

Newspace 463.2.a: $S_{2}^{\mathrm{new}}(\Gamma_0(463))$

Newforms

Label	Dim	Coefficient field	Trace form	AL signs	Sign	CM	Elliptic curve
463.2.a.a	16	degree 16	$16q - 9q^{2} - 6q^{3} + 15q^{4} - 16q^{5} - 6q^{6} - 10q^{7} + O(q^{8})$	+	$-1$
463.2.a.b	22	degree 22	$22q + 8q^{2} + 4q^{3} + 22q^{4} + 14q^{5} + 2q^{7} + O(q^{8})$	−	$+1$

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 $T$
463.2.a.a	$x^{16} + 15x^{15} + 67x^{14} - 17x^{13} - 809x^{12} - 1174x^{11} + 3046x^{10} + 6996x^{9} - 3987x^{8} - 15289x^{7} - 515x^{6} + 13822x^{5} + 4961x^{4} - 3788x^{3} - 2744x^{2} - 573x - 37$
463.2.a.b	$x^{22} - 12x^{21} - 9x^{20} + 618x^{19} - 1499x^{18} - 10987x^{17} + 45307x^{16} + 76458x^{15} - 531576x^{14} - 111388x^{13} + 3234394x^{12} - 1103715x^{11} - 11503686x^{10} + 5843232x^{9} + 25328786x^{8} - 11387828x^{7} - 34340702x^{6} + 9164589x^{5} + 26107615x^{4} - 2037034x^{3} - 9261860x^{2} - 403906x + 953995$

Dimensions

Newforms $S_{2}^{\mathrm{new}}(\Gamma_0(463))$	38
Old forms	0
Cusp forms $S_{2}(\Gamma_0(463))$	38
Eisenstein series $E_{2}(\Gamma_0(463))$	1
Modular forms $M_{2}(\Gamma_0(463))$	39

Decomposition of the old subspace

The old subspace is 0.

Provenance

Stored in the atlas: computed by Sagebrush's modular symbols engine in 0.189 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, 463]: [0, 39] (certified at ell = 2147483647)
T = [(2, 1), (3, 1)]; h of degree 38 = 1 x 38 (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(463, 2)

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

cargo run --release -p sagebrush-web --example atlas -- 463:2 1000

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