Atlas › Modular forms › Weight 2 › Level 944 › 944.2.a

Newspace 944.2.a: $S_{2}^{\mathrm{new}}(\Gamma_0(944))$

Newforms

Label	Dim	Coefficient field	Trace form	AL signs	Elliptic curve
944.2.a.a	1	$\mathbb{Q}$	$q - 3q^{3} - 3q^{5} - 3q^{7} + O(q^{8})$	−	944e1 rank 2
944.2.a.b	1	$\mathbb{Q}$	$q - 2q^{3} - 2q^{5} + 3q^{7} + O(q^{8})$	−	944k1 rank 1
944.2.a.c	1	$\mathbb{Q}$	$q - 2q^{3} + 2q^{5} - q^{7} + O(q^{8})$	+	944c1 rank 1
944.2.a.d	1	$\mathbb{Q}$	$q - 2q^{3} + 2q^{5} + 3q^{7} + O(q^{8})$	+	944g1 rank 0
944.2.a.e	1	$\mathbb{Q}$	$q - q^{3} + 3q^{5} + q^{7} + O(q^{8})$	−	944j1 rank 1
944.2.a.f	1	$\mathbb{Q}$	$q + q^{3} - 3q^{5} + q^{7} + O(q^{8})$	−	944i1 rank 1
944.2.a.g	1	$\mathbb{Q}$	$q + q^{3} - q^{5} - q^{7} + O(q^{8})$	+	944b1 rank 1
944.2.a.h	1	$\mathbb{Q}$	$q + q^{3} - q^{5} - q^{7} + O(q^{8})$	+	944a1 rank 1
944.2.a.i	1	$\mathbb{Q}$	$q + q^{3} - q^{5} + 3q^{7} + O(q^{8})$	+	944f1 rank 0
944.2.a.j	1	$\mathbb{Q}$	$q + q^{3} + q^{5} - 3q^{7} + O(q^{8})$	−	944h1 rank 1
944.2.a.k	1	$\mathbb{Q}$	$q + 3q^{3} - q^{5} - 3q^{7} + O(q^{8})$	−	944d1 rank 0
944.2.a.l	3	degree 3	$3q - 4q^{5} - 8q^{7} + O(q^{8})$	−
944.2.a.m	4	degree 4	$4q + q^{3} - 3q^{5} + 9q^{7} + O(q^{8})$	−
944.2.a.n	5	degree 5	$5q + 2q^{3} + 2q^{5} - 2q^{7} + O(q^{8})$	+
944.2.a.o	6	degree 6	$6q + q^{3} + 7q^{5} + 4q^{7} + O(q^{8})$	−

Hecke characteristic polynomials

The eigenvalue of $T = T_{3} + 3T_{5} + 5T_{11} + 7T_{13} + 9T_{17}$ 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 $T$
944.2.a.a	$x + 102$
944.2.a.b	$x - 39$
944.2.a.c	$x + 17$
944.2.a.d	$x - 11$
944.2.a.e	$x + 104$
944.2.a.f	$x + 30$
944.2.a.g	$x - 10$
944.2.a.h	$x + 70$
944.2.a.i	$x - 26$
944.2.a.j	$x + 66$
944.2.a.k	$x - 8$
944.2.a.l	$x^{3} - 33x^{2} - 2616x + 30249$
944.2.a.m	$x^{4} + 49x^{3} - 2886x^{2} - 13827x + 886226$
944.2.a.n	$x^{5} - 65x^{4} - 3338x^{3} + 155541x^{2} + 1992316x + 5760292$
944.2.a.o	$x^{6} - 226x^{5} + 17423x^{4} - 489793x^{3} + 1374227x^{2} + 77865418x + 286642672$

Dimensions

Newforms $S_{2}^{\mathrm{new}}(\Gamma_0(944))$	29
Old forms	86
Cusp forms $S_{2}(\Gamma_0(944))$	115
Eisenstein series $E_{2}(\Gamma_0(944))$	11
Modular forms $M_{2}(\Gamma_0(944))$	126

Decomposition of the old subspace

$S_{2}^{\mathrm{old}}(\Gamma_0(944)) =$ $S_{2}^{\mathrm{new}}(\Gamma_0(59))^{\oplus 5}$ $\oplus$ $S_{2}^{\mathrm{new}}(\Gamma_0(118))^{\oplus 4}$ $\oplus$ $S_{2}^{\mathrm{new}}(\Gamma_0(236))^{\oplus 3}$ $\oplus$ $S_{2}^{\mathrm{new}}(\Gamma_0(472))^{\oplus 2}$

Provenance

Stored in the atlas: computed by Sagebrush's modular symbols engine in 0.623 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, 8, 16, 59, 118, 236, 472, 944]: [0, 1, 2, 3, 4, 6, 17, 33, 64, 124] (certified at ell = 2147482481)
T = [(3, 1), (5, 3), (11, 5), (13, 7), (17, 9)]; h of degree 29 = 1 x 29 (phi(ord eps) x dim S_k^new); 8 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(944, 2)

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

cargo run --release -p sagebrush-web --example atlas -- 944:2 1000

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