Atlas › Modular forms › Weight 2 › Level 843 › 843.2.a

Newspace 843.2.a: $S_{2}^{\mathrm{new}}(\Gamma_0(843))$

Newforms

Label	Dim	Coefficient field	Trace form	AL signs	Sign	Elliptic curve
843.2.a.a	1	$\mathbb{Q}$	$q + q^{2} - q^{3} - q^{4} - q^{6} + 3q^{7} + O(q^{8})$	+ +	$-1$	843a1 rank 1
843.2.a.b	3	degree 3	$3q - 2q^{2} + 3q^{3} + 6q^{4} - 4q^{5} - 2q^{6} - 4q^{7} + O(q^{8})$	− −	$-1$
843.2.a.c	6	degree 6	$6q - 4q^{2} + 6q^{3} + 2q^{4} - 11q^{5} - 4q^{6} - 2q^{7} + O(q^{8})$	− −	$-1$
843.2.a.d	8	degree 8	$8q - 3q^{2} - 8q^{3} + 5q^{4} - 3q^{5} + 3q^{6} - 9q^{7} + O(q^{8})$	+ +	$-1$
843.2.a.e	14	degree 14	$14q + 6q^{2} + 14q^{3} + 16q^{4} + 13q^{5} + 6q^{6} + O(q^{8})$	− +	$+1$
843.2.a.f	15	degree 15	$15q + 5q^{2} - 15q^{3} + 19q^{4} + 7q^{5} - 5q^{6} + 8q^{7} + O(q^{8})$	+ −	$+1$

Hecke characteristic polynomials

The eigenvalue of $T = T_{2} + T_{5}$ 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 $T$
843.2.a.a	$x - 1$
843.2.a.b	$x^{3} + 6x^{2} + 8x + 1$
843.2.a.c	$x^{6} + 15x^{5} + 77x^{4} + 138x^{3} - 19x^{2} - 182x - 59$
843.2.a.d	$x^{8} + 6x^{7} - x^{6} - 30x^{5} + 4x^{4} + 29x^{3} + 2x^{2} - 5x - 1$
843.2.a.e	$x^{14} - 19x^{13} + 112x^{12} + 2x^{11} - 2413x^{10} + 7412x^{9} + 6223x^{8} - 65750x^{7} + 83567x^{6} + 93244x^{5} - 282508x^{4} + 147619x^{3} + 81776x^{2} - 75708x + 7160$
843.2.a.f	$x^{15} - 12x^{14} - 11x^{13} + 606x^{12} - 1229x^{11} - 10897x^{10} + 37345x^{9} + 78441x^{8} - 424377x^{7} - 68941x^{6} + 2137784x^{5} - 1680647x^{4} - 3754271x^{3} + 5655892x^{2} - 1396348x - 335624$

Dimensions

Newforms $S_{2}^{\mathrm{new}}(\Gamma_0(843))$	47
Old forms	46
Cusp forms $S_{2}(\Gamma_0(843))$	93
Eisenstein series $E_{2}(\Gamma_0(843))$	3
Modular forms $M_{2}(\Gamma_0(843))$	96

Decomposition of the old subspace

$S_{2}^{\mathrm{old}}(\Gamma_0(843)) =$ $S_{2}^{\mathrm{new}}(\Gamma_0(281))^{\oplus 2}$

Provenance

Stored in the atlas: computed by Sagebrush's modular symbols engine in 0.35 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, 281, 843]: [0, 1, 24, 96] (certified at ell = 2147482681)
T = [(2, 1), (5, 1)]; h of degree 47 = 1 x 47 (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(843, 2)

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

cargo run --release -p sagebrush-web --example atlas -- 843:2 1000

← 842.2.a · 844.2.a →