Atlas › Modular forms › Weight 2 › Level 964 › 964.2.a

Newspace 964.2.a: $S_{2}^{\mathrm{new}}(\Gamma_0(964))$

Newforms

Label	Dim	Coefficient field	Trace form	AL signs	Elliptic curve
964.2.a.a	1	$\mathbb{Q}$	$q - 2q^{3} + q^{5} + q^{7} + O(q^{8})$	+	964a1 rank 0
964.2.a.b	7	degree 7	$7q - q^{3} - 8q^{5} + q^{7} + O(q^{8})$	−
964.2.a.c	12	degree 12	$12q + 5q^{3} + 11q^{5} + O(q^{8})$	+

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 $T$
964.2.a.a	$x + 1$
964.2.a.b	$x^{7} + 9x^{6} + 16x^{5} - 24x^{4} - 75x^{3} - 30x^{2} + 27x + 13$
964.2.a.c	$x^{12} - 16x^{11} + 50x^{10} + 416x^{9} - 2862x^{8} + 1349x^{7} + 29852x^{6} - 77539x^{5} + 7854x^{4} + 216718x^{3} - 324543x^{2} + 185504x - 37632$

Dimensions

Newforms $S_{2}^{\mathrm{new}}(\Gamma_0(964))$	20
Old forms	99
Cusp forms $S_{2}(\Gamma_0(964))$	119
Eisenstein series $E_{2}(\Gamma_0(964))$	5
Modular forms $M_{2}(\Gamma_0(964))$	124

Decomposition of the old subspace

$S_{2}^{\mathrm{old}}(\Gamma_0(964)) =$ $S_{2}^{\mathrm{new}}(\Gamma_0(241))^{\oplus 3}$ $\oplus$ $S_{2}^{\mathrm{new}}(\Gamma_0(482))^{\oplus 2}$

Provenance

Stored in the atlas: computed by Sagebrush's modular symbols engine in 0.256 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, 241, 482, 964]: [0, 1, 2, 20, 62, 124] (certified at ell = 2147482801)
T = [(3, 1), (5, 1)]; h of degree 20 = 1 x 20 (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(964, 2)

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

cargo run --release -p sagebrush-web --example atlas -- 964:2 1000

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