Atlas › Modular forms › Weight 2 › Level 956 › 956.2.a

Newspace 956.2.a: $S_{2}^{\mathrm{new}}(\Gamma_0(956))$

Newforms

Label	Dim	Coefficient field	Trace form	AL signs	Elliptic curve
956.2.a.a	1	$\mathbb{Q}$	$q + 3q^{5} - 2q^{7} + O(q^{8})$	+	956a1 rank 0
956.2.a.b	9	degree 9	$9q + 4q^{3} + 9q^{7} + O(q^{8})$	+
956.2.a.c	10	degree 10	$10q - 4q^{3} - 5q^{5} - 9q^{7} + O(q^{8})$	−

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 $T$
956.2.a.a	$x - 3$
956.2.a.b	$x^{9} - 4x^{8} - 49x^{7} + 163x^{6} + 742x^{5} - 1489x^{4} - 3942x^{3} - 303x^{2} + 568x - 64$
956.2.a.c	$x^{10} + 9x^{9} + 3x^{8} - 114x^{7} - 183x^{6} + 213x^{5} + 489x^{4} + 63x^{3} - 171x^{2} - 24x + 16$

Dimensions

Newforms $S_{2}^{\mathrm{new}}(\Gamma_0(956))$	20
Old forms	98
Cusp forms $S_{2}(\Gamma_0(956))$	118
Eisenstein series $E_{2}(\Gamma_0(956))$	5
Modular forms $M_{2}(\Gamma_0(956))$	123

Decomposition of the old subspace

$S_{2}^{\mathrm{old}}(\Gamma_0(956)) =$ $S_{2}^{\mathrm{new}}(\Gamma_0(239))^{\oplus 3}$ $\oplus$ $S_{2}^{\mathrm{new}}(\Gamma_0(478))^{\oplus 2}$

Provenance

Stored in the atlas: computed by Sagebrush's modular symbols engine in 0.254 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, 239, 478, 956]: [0, 1, 2, 21, 62, 123] (certified at ell = 2147482093)
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(956, 2)

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

cargo run --release -p sagebrush-web --example atlas -- 956:2 1000

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