Atlas › Modular forms › Weight 2 › Level 833 › 833.2.a

Newspace 833.2.a: $S_{2}^{\mathrm{new}}(\Gamma_0(833))$

Newforms

Label	Dim	Coefficient field	Trace form	AL signs	Elliptic curve
833.2.a.a	1	$\mathbb{Q}$	$q - q^{2} - q^{4} + 2q^{5} + O(q^{8})$	+	833a1 rank 0
833.2.a.b	3	degree 3	$3q - q^{2} - q^{3} - q^{4} - 2q^{5} + 5q^{6} + O(q^{8})$	−
833.2.a.c	3	degree 3	$3q - q^{2} + q^{3} - q^{4} + 2q^{5} - 5q^{6} + O(q^{8})$	+
833.2.a.d	4	degree 4	$4q - q^{2} - 4q^{3} + 3q^{4} - 7q^{6} + O(q^{8})$	−
833.2.a.e	4	degree 4	$4q - q^{2} - 2q^{3} + 3q^{4} - 2q^{5} - q^{6} + O(q^{8})$	−
833.2.a.f	4	degree 4	$4q - q^{2} + 4q^{3} + 3q^{4} + 7q^{6} + O(q^{8})$	+
833.2.a.g	5	degree 5	$5q + 2q^{2} + 2q^{3} + 10q^{4} + q^{6} + O(q^{8})$	+
833.2.a.h	7	degree 7	$7q + 3q^{2} - q^{3} + 11q^{4} - 2q^{5} - 5q^{6} + O(q^{8})$	+
833.2.a.i	7	degree 7	$7q + 3q^{2} + q^{3} + 11q^{4} + 2q^{5} + 5q^{6} + O(q^{8})$	−
833.2.a.j	8	degree 8	$8q - 2q^{2} - 8q^{3} + 6q^{4} - 4q^{5} + 6q^{6} + O(q^{8})$	+
833.2.a.k	8	degree 8	$8q - 2q^{2} + 8q^{3} + 6q^{4} + 4q^{5} - 6q^{6} + O(q^{8})$	−

Hecke characteristic polynomials

The eigenvalue of $T = T_{2} + 3T_{3} + 5T_{11} + 7T_{13} + 9T_{19}$ 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 $T$
833.2.a.a	$x - 49$
833.2.a.b	$x^{3} - 27x^{2} - 100x + 2939$
833.2.a.c	$x^{3} + 69x^{2} + 908x - 7181$
833.2.a.d	$x^{4} + 149x^{3} + 2897x^{2} - 358201x - 12682977$
833.2.a.e	$x^{4} + 143x^{3} + 6941x^{2} + 126849x + 606907$
833.2.a.f	$x^{4} - 87x^{3} + 1179x^{2} + 62941x - 1409907$
833.2.a.g	$x^{5} + 70x^{4} - 7328x^{3} - 345932x^{2} + 3599490x - 5776273$
833.2.a.h	$x^{7} - 79x^{6} - 10434x^{5} + 970197x^{4} + 15490592x^{3} - 2883552060x^{2} + 59188739840x - 9117342412$
833.2.a.i	$x^{7} + 33x^{6} - 14970x^{5} - 485827x^{4} + 60593108x^{3} + 1162066188x^{2} - 79444032984x + 392958714996$
833.2.a.j	$x^{8} + 234x^{7} + 18165x^{6} + 165104x^{5} - 56163667x^{4} - 3622975132x^{3} - 99356309287x^{2} - 1289672559258x - 6424041799287$
833.2.a.k	$x^{8} - 270x^{7} + 28577x^{6} - 1494688x^{5} + 38684789x^{4} - 357532408x^{3} - 3235951687x^{2} + 75178110990x - 297026166263$

Dimensions

Newforms $S_{2}^{\mathrm{new}}(\Gamma_0(833))$	54
Old forms	23
Cusp forms $S_{2}(\Gamma_0(833))$	77
Eisenstein series $E_{2}(\Gamma_0(833))$	15
Modular forms $M_{2}(\Gamma_0(833))$	92

Decomposition of the old subspace

$S_{2}^{\mathrm{old}}(\Gamma_0(833)) =$ $S_{2}^{\mathrm{new}}(\Gamma_0(17))^{\oplus 3}$ $\oplus$ $S_{2}^{\mathrm{new}}(\Gamma_0(49))^{\oplus 2}$ $\oplus$ $S_{2}^{\mathrm{new}}(\Gamma_0(119))^{\oplus 2}$

Provenance

Stored in the atlas: computed by Sagebrush's modular symbols engine in 0.385 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, 7, 17, 49, 119, 833]: [0, 1, 2, 5, 14, 86] (certified at ell = 2147480161)
T = [(2, 1), (3, 3), (11, 5), (13, 7), (19, 9)]; h of degree 54 = 1 x 54 (phi(ord eps) x dim S_k^new); 14 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(833, 2)

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

cargo run --release -p sagebrush-web --example atlas -- 833:2 1000

← 832.2.a · 834.2.a →