Atlas › Modular forms › Weight 2 › Level 466 › 466.2.a

Newspace 466.2.a: $S_{2}^{\mathrm{new}}(\Gamma_0(466))$

Newforms

Label	Dim	Coefficient field	Trace form	AL signs	Sign	Elliptic curve
466.2.a.a	1	$\mathbb{Q}$	$q - q^{2} + 2q^{3} + q^{4} - 2q^{6} + O(q^{8})$	+ −	$+1$	466a1 rank 0
466.2.a.b	1	$\mathbb{Q}$	$q + q^{2} + q^{3} + q^{4} + q^{6} + 2q^{7} + O(q^{8})$	− +	$+1$	466b1 rank 0
466.2.a.c	3	degree 3	$3q - 3q^{2} - 2q^{3} + 3q^{4} + 5q^{5} + 2q^{6} + 3q^{7} + O(q^{8})$	+ −	$+1$
466.2.a.d	3	degree 3	$3q + 3q^{2} - 4q^{3} + 3q^{4} - 7q^{5} - 4q^{6} - q^{7} + O(q^{8})$	− −	$-1$
466.2.a.e	5	degree 5	$5q - 5q^{2} + 5q^{4} - 5q^{5} - 5q^{7} + O(q^{8})$	+ +	$-1$
466.2.a.f	6	degree 6	$6q + 6q^{2} + q^{3} + 6q^{4} + 7q^{5} + q^{6} - 3q^{7} + O(q^{8})$	− +	$+1$

Hecke characteristic polynomials

The eigenvalue of $T = T_{3} + T_{5}$ 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 $T$
466.2.a.a	$x - 2$
466.2.a.b	$x - 1$
466.2.a.c	$x^{3} - 3x^{2} - 10x - 1$
466.2.a.d	$x^{3} + 11x^{2} + 38x + 41$
466.2.a.e	$x^{5} + 5x^{4} - x^{3} - 38x^{2} - 60x - 25$
466.2.a.f	$x^{6} - 8x^{5} + 3x^{4} + 89x^{3} - 93x^{2} - 266x + 202$

Dimensions

Newforms $S_{2}^{\mathrm{new}}(\Gamma_0(466))$	19
Old forms	38
Cusp forms $S_{2}(\Gamma_0(466))$	57
Eisenstein series $E_{2}(\Gamma_0(466))$	3
Modular forms $M_{2}(\Gamma_0(466))$	60

Decomposition of the old subspace

$S_{2}^{\mathrm{old}}(\Gamma_0(466)) =$ $S_{2}^{\mathrm{new}}(\Gamma_0(233))^{\oplus 2}$

Provenance

Stored in the atlas: computed by Sagebrush's modular symbols engine in 0.197 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, 2, 233, 466]: [0, 1, 20, 60] (certified at ell = 2147482481)
T = [(3, 1), (5, 1)]; h of degree 19 = 1 x 19 (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(466, 2)

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

cargo run --release -p sagebrush-web --example atlas -- 466:2 1000

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