Atlas › Modular forms › Weight 2 › Level 460 › 460.2.a

Newspace 460.2.a: $S_{2}^{\mathrm{new}}(\Gamma_0(460))$

Newforms

Label	Dim	Coefficient field	Trace form	AL signs	Elliptic curve
460.2.a.a	1	$\mathbb{Q}$	$q - q^{3} + q^{5} - 2q^{7} + O(q^{8})$	− +	460d1 rank 1
460.2.a.b	1	$\mathbb{Q}$	$q - q^{5} - q^{7} + O(q^{8})$	+ +	460a1 rank 0
460.2.a.c	1	$\mathbb{Q}$	$q + q^{3} - q^{5} - 4q^{7} + O(q^{8})$	+ −	460c1 rank 1
460.2.a.d	1	$\mathbb{Q}$	$q + 3q^{3} - q^{5} + 2q^{7} + O(q^{8})$	+ +	460b1 rank 0
460.2.a.e	2	$\mathbb{Q}(\sqrt{17})$	$2q + q^{3} + 2q^{5} + q^{7} + O(q^{8})$	− −

Hecke characteristic polynomials

The eigenvalue of $T = T_{3} + 3T_{7}$ 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 $T$
460.2.a.a	$x + 7$
460.2.a.b	$x + 3$
460.2.a.c	$x + 11$
460.2.a.d	$x - 9$
460.2.a.e	$x^{2} - 4x - 13$

Dimensions

Newforms $S_{2}^{\mathrm{new}}(\Gamma_0(460))$	6
Old forms	61
Cusp forms $S_{2}(\Gamma_0(460))$	67
Eisenstein series $E_{2}(\Gamma_0(460))$	11
Modular forms $M_{2}(\Gamma_0(460))$	78

Decomposition of the old subspace

$S_{2}^{\mathrm{old}}(\Gamma_0(460)) =$ $S_{2}^{\mathrm{new}}(\Gamma_0(20))^{\oplus 2}$ $\oplus$ $S_{2}^{\mathrm{new}}(\Gamma_0(23))^{\oplus 6}$ $\oplus$ $S_{2}^{\mathrm{new}}(\Gamma_0(46))^{\oplus 4}$ $\oplus$ $S_{2}^{\mathrm{new}}(\Gamma_0(92))^{\oplus 2}$ $\oplus$ $S_{2}^{\mathrm{new}}(\Gamma_0(115))^{\oplus 3}$ $\oplus$ $S_{2}^{\mathrm{new}}(\Gamma_0(230))^{\oplus 2}$

Provenance

Stored in the atlas: computed by Sagebrush's modular symbols engine in 0.243 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, 4, 5, 10, 20, 23, 46, 92, 115, 230, 460]: [0, 1, 2, 1, 3, 6, 3, 8, 15, 14, 40, 78] (certified at ell = 2147483053)
T = [(3, 1), (7, 3)]; h of degree 6 = 1 x 6 (phi(ord eps) x dim S_k^new); 1 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(460, 2)

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

cargo run --release -p sagebrush-web --example atlas -- 460:2 1000

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