Atlas › Modular forms › Weight 2 › Level 945 › 945.2.a

Newspace 945.2.a: $S_{2}^{\mathrm{new}}(\Gamma_0(945))$

Newforms

Label	Dim	Coefficient field	Trace form	AL signs
945.2.a.a	2	$\mathbb{Q}(\sqrt{5})$	$2q - 3q^{2} + 3q^{4} + 2q^{5} + 2q^{7} + O(q^{8})$	− −
945.2.a.b	2	$\mathbb{Q}(\sqrt{2})$	$2q - 2q^{2} + 2q^{4} - 2q^{5} - 2q^{7} + O(q^{8})$	+ +
945.2.a.c	2	$\mathbb{Q}(\sqrt{5})$	$2q - q^{2} - q^{4} + 2q^{5} - 2q^{7} + O(q^{8})$	− +
945.2.a.d	2	$\mathbb{Q}(\sqrt{5})$	$2q - q^{2} - q^{4} + 2q^{5} - 2q^{7} + O(q^{8})$	− +
945.2.a.e	2	$\mathbb{Q}(\sqrt{5})$	$2q - q^{2} - q^{4} + 2q^{5} - 2q^{7} + O(q^{8})$	− +
945.2.a.f	2	$\mathbb{Q}(\sqrt{13})$	$2q - q^{2} + 3q^{4} - 2q^{5} + 2q^{7} + O(q^{8})$	+ −
945.2.a.g	2	$\mathbb{Q}(\sqrt{5})$	$2q + q^{2} - q^{4} - 2q^{5} - 2q^{7} + O(q^{8})$	+ +
945.2.a.h	2	$\mathbb{Q}(\sqrt{5})$	$2q + q^{2} - q^{4} - 2q^{5} - 2q^{7} + O(q^{8})$	+ +
945.2.a.i	2	$\mathbb{Q}(\sqrt{5})$	$2q + q^{2} - q^{4} - 2q^{5} - 2q^{7} + O(q^{8})$	+ +
945.2.a.j	2	$\mathbb{Q}(\sqrt{13})$	$2q + q^{2} + 3q^{4} + 2q^{5} + 2q^{7} + O(q^{8})$	− −
945.2.a.k	2	$\mathbb{Q}(\sqrt{2})$	$2q + 2q^{2} + 2q^{4} + 2q^{5} - 2q^{7} + O(q^{8})$	− +
945.2.a.l	2	$\mathbb{Q}(\sqrt{5})$	$2q + 3q^{2} + 3q^{4} - 2q^{5} + 2q^{7} + O(q^{8})$	+ −
945.2.a.m	4	degree 4	$4q - q^{2} + 9q^{4} - 4q^{5} + 4q^{7} + O(q^{8})$	+ −
945.2.a.n	4	degree 4	$4q + q^{2} + 9q^{4} + 4q^{5} + 4q^{7} + O(q^{8})$	− −

Hecke characteristic polynomials

The eigenvalue of $T = T_{2} + 3T_{11}$ 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 $T$
945.2.a.a	$x^{2} + 15x + 25$
945.2.a.b	$x^{2} - 4x - 28$
945.2.a.c	$x^{2} + 7x - 19$
945.2.a.d	$x^{2} + 7x - 199$
945.2.a.e	$x^{2} - 11x - 1$
945.2.a.f	$x^{2} + 19x + 87$
945.2.a.g	$x^{2} + 11x - 1$
945.2.a.h	$x^{2} - 7x - 19$
945.2.a.i	$x^{2} - 7x - 199$
945.2.a.j	$x^{2} - 19x + 87$
945.2.a.k	$x^{2} + 4x - 28$
945.2.a.l	$x^{2} - 15x + 25$
945.2.a.m	$x^{4} - 11x^{3} - 167x^{2} + 136x + 1800$
945.2.a.n	$x^{4} + 11x^{3} - 167x^{2} - 136x + 1800$

Dimensions

Newforms $S_{2}^{\mathrm{new}}(\Gamma_0(945))$	32
Old forms	101
Cusp forms $S_{2}(\Gamma_0(945))$	133
Eisenstein series $E_{2}(\Gamma_0(945))$	23
Modular forms $M_{2}(\Gamma_0(945))$	156

Decomposition of the old subspace

Provenance

Stored in the atlas: computed by Sagebrush's modular symbols engine in 0.547 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, 3, 5, 7, 9, 15, 21, 27, 35, 45, 63, 105, 135, 189, 315, 945]: [0, 1, 1, 1, 2, 4, 4, 4, 6, 8, 10, 20, 20, 26, 52, 148] (certified at ell = 2147483629)
T = [(2, 1), (11, 3)]; h of degree 32 = 1 x 32 (phi(ord eps) x dim S_k^new); 5 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(945, 2)

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

cargo run --release -p sagebrush-web --example atlas -- 945:2 1000

← 944.2.a · 946.2.a →