Atlas › Modular forms › Weight 2 › Level 954 › 954.2.a

Newspace 954.2.a: $S_{2}^{\mathrm{new}}(\Gamma_0(954))$

Newforms

Label	Dim	Coefficient field	Trace form	AL signs	Elliptic curve
954.2.a.a	1	$\mathbb{Q}$	$q - q^{2} + q^{4} - 3q^{5} + 2q^{7} + O(q^{8})$	+ −	954f1 rank 1
954.2.a.b	1	$\mathbb{Q}$	$q - q^{2} + q^{4} - 2q^{5} + 4q^{7} + O(q^{8})$	+ −	954b1 rank 0
954.2.a.c	1	$\mathbb{Q}$	$q - q^{2} + q^{4} - 4q^{7} + O(q^{8})$	+ −	954e1 rank 1
954.2.a.d	1	$\mathbb{Q}$	$q - q^{2} + q^{4} + q^{7} + O(q^{8})$	+ −	954d1 rank 1
954.2.a.e	1	$\mathbb{Q}$	$q - q^{2} + q^{4} + 2q^{5} - 3q^{7} + O(q^{8})$	+ +	954a1 rank 1
954.2.a.f	1	$\mathbb{Q}$	$q - q^{2} + q^{4} + 3q^{5} - 4q^{7} + O(q^{8})$	+ +	954c1 rank 0
954.2.a.g	1	$\mathbb{Q}$	$q + q^{2} + q^{4} - 4q^{5} + q^{7} + O(q^{8})$	− +	954j1 rank 1
954.2.a.h	1	$\mathbb{Q}$	$q + q^{2} + q^{4} - 2q^{5} - 3q^{7} + O(q^{8})$	− −	954h1 rank 1
954.2.a.i	1	$\mathbb{Q}$	$q + q^{2} + q^{4} - q^{5} - 2q^{7} + O(q^{8})$	− +	954i1 rank 1
954.2.a.j	1	$\mathbb{Q}$	$q + q^{2} + q^{4} + 5q^{7} + O(q^{8})$	− −	954k1 rank 0
954.2.a.k	1	$\mathbb{Q}$	$q + q^{2} + q^{4} + q^{5} + O(q^{8})$	− −	954l1 rank 0
954.2.a.l	1	$\mathbb{Q}$	$q + q^{2} + q^{4} + 2q^{5} + 4q^{7} + O(q^{8})$	− +	954g1 rank 0
954.2.a.m	1	$\mathbb{Q}$	$q + q^{2} + q^{4} + 4q^{5} + O(q^{8})$	− −	954m1 rank 0
954.2.a.n	2	$\mathbb{Q}(\sqrt{17})$	$2q - 2q^{2} + 2q^{4} - q^{5} + q^{7} + O(q^{8})$	+ +
954.2.a.o	2	$\mathbb{Q}(\sqrt{41})$	$2q + 2q^{2} + 2q^{4} - q^{5} + O(q^{8})$	− −
954.2.a.p	3	degree 3	$3q - 3q^{2} + 3q^{4} - 3q^{7} + O(q^{8})$	+ −
954.2.a.q	3	degree 3	$3q + 3q^{2} + 3q^{4} - 3q^{7} + O(q^{8})$	− +

Hecke characteristic polynomials

The eigenvalue of $T = T_{5} + 3T_{7} + 5T_{11} + 7T_{13} + 9T_{17}$ 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 $T$
954.2.a.a	$x + 37$
954.2.a.b	$x - 34$
954.2.a.c	$x - 50$
954.2.a.d	$x + 40$
954.2.a.e	$x + 8$
954.2.a.f	$x + 43$
954.2.a.g	$x + 78$
954.2.a.h	$x + 38$
954.2.a.i	$x + 87$
954.2.a.j	$x + 52$
954.2.a.k	$x - 55$
954.2.a.l	$x - 18$
954.2.a.m	$x + 14$
954.2.a.n	$x^{2} - 43x + 118$
954.2.a.o	$x^{2} - 149x + 3818$
954.2.a.p	$x^{3} + 36x^{2} - 2079x + 18130$
954.2.a.q	$x^{3} - 102x^{2} + 2613x - 18572$

Dimensions

Newforms $S_{2}^{\mathrm{new}}(\Gamma_0(954))$	23
Old forms	132
Cusp forms $S_{2}(\Gamma_0(954))$	155
Eisenstein series $E_{2}(\Gamma_0(954))$	15
Modular forms $M_{2}(\Gamma_0(954))$	170

Decomposition of the old subspace

$S_{2}^{\mathrm{old}}(\Gamma_0(954)) =$ $S_{2}^{\mathrm{new}}(\Gamma_0(53))^{\oplus 6}$ $\oplus$ $S_{2}^{\mathrm{new}}(\Gamma_0(106))^{\oplus 3}$ $\oplus$ $S_{2}^{\mathrm{new}}(\Gamma_0(159))^{\oplus 4}$ $\oplus$ $S_{2}^{\mathrm{new}}(\Gamma_0(318))^{\oplus 2}$ $\oplus$ $S_{2}^{\mathrm{new}}(\Gamma_0(477))^{\oplus 2}$

Provenance

Stored in the atlas: computed by Sagebrush's modular symbols engine in 0.761 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, 3, 6, 9, 18, 53, 106, 159, 318, 477, 954]: [0, 1, 1, 3, 2, 5, 5, 15, 20, 58, 56, 166] (certified at ell = 2147483053)
T = [(5, 1), (7, 3), (11, 5), (13, 7), (17, 9)]; h of degree 23 = 1 x 23 (phi(ord eps) x dim S_k^new); 6 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(954, 2)

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

cargo run --release -p sagebrush-web --example atlas -- 954:2 1000

← 953.2.a · 955.2.a →