Atlas › Modular forms › Weight 2 › Level 834 › 834.2.a

Newspace 834.2.a: $S_{2}^{\mathrm{new}}(\Gamma_0(834))$

Newforms

Label	Dim	Coefficient field	Trace form	AL signs	Sign	Elliptic curve
834.2.a.a	1	$\mathbb{Q}$	$q - q^{2} + q^{3} + q^{4} - 3q^{5} - q^{6} + q^{7} + O(q^{8})$	+ − −	$-1$	834c1 rank 1
834.2.a.b	1	$\mathbb{Q}$	$q - q^{2} + q^{3} + q^{4} + 2q^{5} - q^{6} + O(q^{8})$	+ − +	$+1$	834a1 rank 0
834.2.a.c	1	$\mathbb{Q}$	$q - q^{2} + q^{3} + q^{4} + 2q^{5} - q^{6} + O(q^{8})$	+ − +	$+1$	834b1 rank 0
834.2.a.d	1	$\mathbb{Q}$	$q + q^{2} - q^{3} + q^{4} - 3q^{5} - q^{6} + q^{7} + O(q^{8})$	− + −	$-1$	834f1 rank 1
834.2.a.e	1	$\mathbb{Q}$	$q + q^{2} - q^{3} + q^{4} - q^{6} - 2q^{7} + O(q^{8})$	− + −	$-1$	834e1 rank 1
834.2.a.f	1	$\mathbb{Q}$	$q + q^{2} - q^{3} + q^{4} - q^{6} + 4q^{7} + O(q^{8})$	− + +	$+1$	834d1 rank 0
834.2.a.g	1	$\mathbb{Q}$	$q + q^{2} + q^{3} + q^{4} - 4q^{5} + q^{6} - 2q^{7} + O(q^{8})$	− − +	$-1$	834g1 rank 1
834.2.a.h	2	$\mathbb{Q}(\sqrt{2})$	$2q - 2q^{2} - 2q^{3} + 2q^{4} + 2q^{6} - 4q^{7} + O(q^{8})$	+ + +	$-1$
834.2.a.i	2	$\mathbb{Q}(\sqrt{6})$	$2q - 2q^{2} + 2q^{3} + 2q^{4} - 2q^{6} - 4q^{7} + O(q^{8})$	+ − −	$-1$
834.2.a.j	2	$\mathbb{Q}(\sqrt{3})$	$2q + 2q^{2} + 2q^{3} + 2q^{4} - 2q^{5} + 2q^{6} + 2q^{7} + O(q^{8})$	− − −	$+1$
834.2.a.k	3	degree 3	$3q + 3q^{2} - 3q^{3} + 3q^{4} + 2q^{5} - 3q^{6} - 2q^{7} + O(q^{8})$	− + +	$+1$
834.2.a.l	3	degree 3	$3q + 3q^{2} + 3q^{3} + 3q^{4} + 7q^{5} + 3q^{6} - 3q^{7} + O(q^{8})$	− − −	$+1$
834.2.a.m	4	degree 4	$4q - 4q^{2} - 4q^{3} + 4q^{4} - 3q^{5} + 4q^{6} + 5q^{7} + O(q^{8})$	+ + −	$+1$

Hecke characteristic polynomials

The eigenvalue of $T = T_{5} + 3T_{7} + 5T_{17} + 7T_{19} + 9T_{23}$ 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 $T$
834.2.a.a	$x - 8$
834.2.a.b	$x - 60$
834.2.a.c	$x - 48$
834.2.a.d	$x + 92$
834.2.a.e	$x - 58$
834.2.a.f	$x - 22$
834.2.a.g	$x + 44$
834.2.a.h	$x^{2} + 44x - 574$
834.2.a.i	$x^{2} + 200x + 9850$
834.2.a.j	$x^{2} - 134x + 3406$
834.2.a.k	$x^{3} - 92x^{2} - 194x + 47972$
834.2.a.l	$x^{3} + 82x^{2} - 7110x + 71096$
834.2.a.m	$x^{4} - 8x^{3} - 5158x^{2} - 157036x - 1075232$

Dimensions

Newforms $S_{2}^{\mathrm{new}}(\Gamma_0(834))$	23
Old forms	114
Cusp forms $S_{2}(\Gamma_0(834))$	137
Eisenstein series $E_{2}(\Gamma_0(834))$	7
Modular forms $M_{2}(\Gamma_0(834))$	144

Decomposition of the old subspace

$S_{2}^{\mathrm{old}}(\Gamma_0(834)) =$ $S_{2}^{\mathrm{new}}(\Gamma_0(139))^{\oplus 4}$ $\oplus$ $S_{2}^{\mathrm{new}}(\Gamma_0(278))^{\oplus 2}$ $\oplus$ $S_{2}^{\mathrm{new}}(\Gamma_0(417))^{\oplus 2}$

Provenance

Stored in the atlas: computed by Sagebrush's modular symbols engine in 0.524 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, 139, 278, 417, 834]: [0, 1, 1, 3, 12, 37, 48, 144] (certified at ell = 2147483137)
T = [(5, 1), (7, 3), (17, 5), (19, 7), (23, 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(834, 2)

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

cargo run --release -p sagebrush-web --example atlas -- 834:2 1000

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