Atlas › Modular forms › Weight 2 › Level 818 › 818.2.a

Newspace 818.2.a: $S_{2}^{\mathrm{new}}(\Gamma_0(818))$

Newforms

Label	Dim	Coefficient field	Trace form	AL signs	Sign
818.2.a.a	4	degree 4	$4q + 4q^{2} - 2q^{3} + 4q^{4} - 5q^{5} - 2q^{6} - 7q^{7} + O(q^{8})$	− −	$-1$
818.2.a.b	7	degree 7	$7q - 7q^{2} - 4q^{3} + 7q^{4} + q^{5} + 4q^{6} - 11q^{7} + O(q^{8})$	+ +	$-1$
818.2.a.c	10	degree 10	$10q - 10q^{2} + 2q^{3} + 10q^{4} - 5q^{5} - 2q^{6} + 13q^{7} + O(q^{8})$	+ −	$+1$
818.2.a.d	14	degree 14	$14q + 14q^{2} + 4q^{3} + 14q^{4} + 7q^{5} + 4q^{6} + 9q^{7} + O(q^{8})$	− +	$+1$

Hecke characteristic polynomials

The eigenvalue of $T = T_{3} + T_{5}$ 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 $T$
818.2.a.a	$x^{4} + 7x^{3} + 15x^{2} + 9x - 1$
818.2.a.b	$x^{7} + 3x^{6} - 15x^{5} - 19x^{4} + 71x^{3} + 14x^{2} - 108x + 52$
818.2.a.c	$x^{10} + 3x^{9} - 58x^{8} - 156x^{7} + 1062x^{6} + 2657x^{5} - 7034x^{4} - 16403x^{3} + 11709x^{2} + 21679x - 9803$
818.2.a.d	$x^{14} - 11x^{13} - 14x^{12} + 584x^{11} - 1800x^{10} - 5685x^{9} + 40984x^{8} - 62217x^{7} - 54559x^{6} + 219473x^{5} - 109813x^{4} - 142104x^{3} + 155484x^{2} - 42800x + 2500$

Dimensions

Newforms $S_{2}^{\mathrm{new}}(\Gamma_0(818))$	35
Old forms	66
Cusp forms $S_{2}(\Gamma_0(818))$	101
Eisenstein series $E_{2}(\Gamma_0(818))$	3
Modular forms $M_{2}(\Gamma_0(818))$	104

Decomposition of the old subspace

$S_{2}^{\mathrm{old}}(\Gamma_0(818)) =$ $S_{2}^{\mathrm{new}}(\Gamma_0(409))^{\oplus 2}$

Provenance

Stored in the atlas: computed by Sagebrush's modular symbols engine in 0.246 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, 409, 818]: [0, 1, 34, 104] (certified at ell = 2147477809)
T = [(3, 1), (5, 1)]; h of degree 35 = 1 x 35 (phi(ord eps) x dim S_k^new); 4 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(818, 2)

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

cargo run --release -p sagebrush-web --example atlas -- 818:2 1000

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