Atlas › Modular forms › Weight 2 › Level 796 › 796.2.a

Newspace 796.2.a: $S_{2}^{\mathrm{new}}(\Gamma_0(796))$

Newforms

Label	Dim	Coefficient field	Trace form	AL signs
796.2.a.a	3	degree 3	$3q + q^{7} + O(q^{8})$	−
796.2.a.b	5	degree 5	$5q - 4q^{3} - 6q^{5} - 5q^{7} + O(q^{8})$	−
796.2.a.c	8	degree 8	$8q + 2q^{3} + 2q^{5} + 4q^{7} + O(q^{8})$	+

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 $T$
796.2.a.a	$x^{3} - 7x - 7$
796.2.a.b	$x^{5} + 10x^{4} + 26x^{3} + 20x^{2} - 2x - 3$
796.2.a.c	$x^{8} - 4x^{7} - 39x^{6} + 155x^{5} + 408x^{4} - 1605x^{3} - 952x^{2} + 3083x + 1885$

Dimensions

Newforms $S_{2}^{\mathrm{new}}(\Gamma_0(796))$	16
Old forms	82
Cusp forms $S_{2}(\Gamma_0(796))$	98
Eisenstein series $E_{2}(\Gamma_0(796))$	5
Modular forms $M_{2}(\Gamma_0(796))$	103

Decomposition of the old subspace

$S_{2}^{\mathrm{old}}(\Gamma_0(796)) =$ $S_{2}^{\mathrm{new}}(\Gamma_0(199))^{\oplus 3}$ $\oplus$ $S_{2}^{\mathrm{new}}(\Gamma_0(398))^{\oplus 2}$

Provenance

Stored in the atlas: computed by Sagebrush's modular symbols engine in 0.228 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, 4, 199, 398, 796]: [0, 1, 2, 17, 52, 103] (certified at ell = 2147483647)
T = [(3, 1), (5, 1)]; h of degree 16 = 1 x 16 (phi(ord eps) x dim S_k^new); 2 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(796, 2)

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

cargo run --release -p sagebrush-web --example atlas -- 796:2 1000

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