Atlas › Modular forms › Weight 2 › Level 873 › 873.2.a

Newspace 873.2.a: $S_{2}^{\mathrm{new}}(\Gamma_0(873))$

Newforms

Label	Dim	Coefficient field	Trace form	AL signs	Elliptic curve
873.2.a.a	1	$\mathbb{Q}$	$q - 2q^{2} + 2q^{4} - q^{5} + 2q^{7} + O(q^{8})$	−	873d1 rank 1
873.2.a.b	1	$\mathbb{Q}$	$q + q^{2} - q^{4} + 2q^{7} + O(q^{8})$	+	873a1 rank 0
873.2.a.c	1	$\mathbb{Q}$	$q + q^{2} - q^{4} + 2q^{5} - 4q^{7} + O(q^{8})$	−	873b1 rank 1
873.2.a.d	1	$\mathbb{Q}$	$q + 2q^{2} + 2q^{4} - 3q^{5} - 2q^{7} + O(q^{8})$	−	873c1 rank 1
873.2.a.e	2	$\mathbb{Q}(\sqrt{5})$	$2q - 3q^{2} + 3q^{4} - 6q^{5} - 3q^{7} + O(q^{8})$	−
873.2.a.f	2	$\mathbb{Q}(\sqrt{5})$	$2q + q^{2} - q^{4} + 4q^{5} - 7q^{7} + O(q^{8})$	−
873.2.a.g	2	$\mathbb{Q}(\sqrt{13})$	$2q + q^{2} + 3q^{4} + 6q^{5} + 3q^{7} + O(q^{8})$	+
873.2.a.h	3	degree 3	$3q + 4q^{2} + 4q^{4} + 3q^{5} - 7q^{7} + O(q^{8})$	+
873.2.a.i	4	degree 4	$4q - 3q^{2} + 3q^{4} - q^{5} + 3q^{7} + O(q^{8})$	−
873.2.a.j	6	degree 6	$6q + 2q^{4} - 14q^{7} + O(q^{8})$	+
873.2.a.k	7	degree 7	$7q + 8q^{4} - 4q^{5} + 9q^{7} + O(q^{8})$	+
873.2.a.l	10	degree 10	$10q + 14q^{4} + 22q^{7} + O(q^{8})$	−

Hecke characteristic polynomials

The eigenvalue of $T = T_{2} + 3T_{5} + 5T_{7} + 7T_{11}$ 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 $T$
873.2.a.a	$x + 23$
873.2.a.b	$x - 39$
873.2.a.c	$x + 41$
873.2.a.d	$x + 17$
873.2.a.e	$x^{2} - 13x - 59$
873.2.a.f	$x^{2} + 29x + 59$
873.2.a.g	$x^{2} - 55x + 753$
873.2.a.h	$x^{3} - 27x^{2} - 226x + 6131$
873.2.a.i	$x^{4} + 26x^{3} - 1339x^{2} - 17519x + 520133$
873.2.a.j	$x^{6} + 70x^{5} - 660x^{4} - 84570x^{3} + 218896x^{2} + 18657960x - 94821611$
873.2.a.k	$x^{7} - 54x^{6} - 2148x^{5} + 162957x^{4} - 2315753x^{3} - 10152018x^{2} + 280943548x - 109529701$
873.2.a.l	$x^{10} - 110x^{9} + 960x^{8} + 224250x^{7} - 5999485x^{6} - 38702890x^{5} + 1947344985x^{4} - 1849844330x^{3} - 185867526156x^{2} + 289565538760x + 5633396201887$

Dimensions

Newforms $S_{2}^{\mathrm{new}}(\Gamma_0(873))$	40
Old forms	55
Cusp forms $S_{2}(\Gamma_0(873))$	95
Eisenstein series $E_{2}(\Gamma_0(873))$	7
Modular forms $M_{2}(\Gamma_0(873))$	102

Decomposition of the old subspace

$S_{2}^{\mathrm{old}}(\Gamma_0(873)) =$ $S_{2}^{\mathrm{new}}(\Gamma_0(97))^{\oplus 3}$ $\oplus$ $S_{2}^{\mathrm{new}}(\Gamma_0(291))^{\oplus 2}$

Provenance

Stored in the atlas: computed by Sagebrush's modular symbols engine in 0.427 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, 9, 97, 291, 873]: [0, 1, 2, 8, 34, 100] (certified at ell = 2147483137)
T = [(2, 1), (5, 3), (7, 5), (11, 7)]; h of degree 40 = 1 x 40 (phi(ord eps) x dim S_k^new); 9 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(873, 2)

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

cargo run --release -p sagebrush-web --example atlas -- 873:2 1000

← 872.2.a · 874.2.a →