Atlas › Modular forms › Weight 2 › Level 920 › 920.2.a

Newspace 920.2.a: $S_{2}^{\mathrm{new}}(\Gamma_0(920))$

Newforms

Label	Dim	Coefficient field	Trace form	AL signs	Elliptic curve
920.2.a.a	1	$\mathbb{Q}$	$q - 3q^{3} + q^{5} - 2q^{7} + O(q^{8})$	− −	920b1 rank 1
920.2.a.b	1	$\mathbb{Q}$	$q - q^{3} + q^{5} + O(q^{8})$	− +	920d1 rank 1
920.2.a.c	1	$\mathbb{Q}$	$q + q^{5} + q^{7} + O(q^{8})$	− −	920a1 rank 1
920.2.a.d	1	$\mathbb{Q}$	$q + q^{3} - q^{5} - 2q^{7} + O(q^{8})$	+ −	920c1 rank 1
920.2.a.e	2	$\mathbb{Q}(\sqrt{17})$	$2q - q^{3} - 2q^{5} - q^{7} + O(q^{8})$	+ +
920.2.a.f	2	$\mathbb{Q}(\sqrt{17})$	$2q + q^{3} + 2q^{5} + 2q^{7} + O(q^{8})$	− −
920.2.a.g	3	degree 3	$3q - 3q^{5} + 3q^{7} + O(q^{8})$	+ −
920.2.a.h	3	degree 3	$3q + q^{3} + 3q^{5} + 2q^{7} + O(q^{8})$	− −
920.2.a.i	3	degree 3	$3q + 2q^{3} + 3q^{5} + 7q^{7} + O(q^{8})$	− +
920.2.a.j	5	degree 5	$5q - 5q^{5} - 2q^{7} + O(q^{8})$	+ +

Hecke characteristic polynomials

The eigenvalue of $T = T_{3} + 3T_{7} + 5T_{11} + 7T_{29} + 9T_{31} + 11T_{37}$ 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 $T$
920.2.a.a	$x + 91$
920.2.a.b	$x - 29$
920.2.a.c	$x + 22$
920.2.a.d	$x + 123$
920.2.a.e	$x^{2} + 185x + 7838$
920.2.a.f	$x^{2} + 127x - 52$
920.2.a.g	$x^{3} - 231x^{2} + 12750x - 43292$
920.2.a.h	$x^{3} - 116x^{2} - 9216x + 1023688$
920.2.a.i	$x^{3} - 143x^{2} + 3814x + 7244$
920.2.a.j	$x^{5} - 353x^{4} + 41000x^{3} - 1492120x^{2} - 17505912x + 985394848$

Dimensions

Newforms $S_{2}^{\mathrm{new}}(\Gamma_0(920))$	22
Old forms	115
Cusp forms $S_{2}(\Gamma_0(920))$	137
Eisenstein series $E_{2}(\Gamma_0(920))$	15
Modular forms $M_{2}(\Gamma_0(920))$	152

Decomposition of the old subspace

Provenance

Stored in the atlas: computed by Sagebrush's modular symbols engine in 0.942 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, 8, 10, 20, 23, 40, 46, 92, 115, 184, 230, 460, 920]: [0, 1, 2, 1, 3, 3, 6, 3, 10, 8, 15, 14, 28, 40, 78, 152] (certified at ell = 2147483053)
T = [(3, 1), (7, 3), (11, 5), (29, 7), (31, 9), (37, 11)]; h of degree 22 = 1 x 22 (phi(ord eps) x dim S_k^new); 7 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(920, 2)

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

cargo run --release -p sagebrush-web --example atlas -- 920:2 1000

← 919.2.a · 921.2.a →