Atlas › Modular forms › Weight 2 › Level 579 › 579.2.a

Newspace 579.2.a: $S_{2}^{\mathrm{new}}(\Gamma_0(579))$

Newforms

Label	Dim	Coefficient field	Trace form	AL signs	Sign	Elliptic curve
579.2.a.a	1	$\mathbb{Q}$	$q - q^{2} + q^{3} - q^{4} - q^{6} + O(q^{8})$	− −	$-1$	579b1 rank 1
579.2.a.b	1	$\mathbb{Q}$	$q + 2q^{2} - q^{3} + 2q^{4} + 2q^{5} - 2q^{6} + q^{7} + O(q^{8})$	+ −	$+1$	579a1 rank 0
579.2.a.c	2	$\mathbb{Q}(\sqrt{2})$	$2q - 2q^{2} - 2q^{3} - 2q^{4} - 4q^{5} + 2q^{6} + 4q^{7} + O(q^{8})$	+ +	$-1$
579.2.a.d	3	degree 3	$3q - 3q^{3} + 4q^{4} - 4q^{5} + 3q^{7} + O(q^{8})$	+ +	$-1$
579.2.a.e	3	degree 3	$3q + 3q^{3} - 6q^{5} - 9q^{7} + O(q^{8})$	− −	$-1$
579.2.a.f	10	degree 10	$10q + 2q^{2} - 10q^{3} + 14q^{4} + 8q^{5} - 2q^{6} - 10q^{7} + O(q^{8})$	+ −	$+1$
579.2.a.g	13	degree 13	$13q + 2q^{2} + 13q^{3} + 18q^{4} + 6q^{5} + 2q^{6} + 15q^{7} + O(q^{8})$	− +	$+1$

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 $T$
579.2.a.a	$x + 1$
579.2.a.b	$x - 4$
579.2.a.c	$x^{2} + 6x + 7$
579.2.a.d	$x^{3} + 4x^{2} - 3x - 9$
579.2.a.e	$x^{3} + 6x^{2} + 9x + 1$
579.2.a.f	$x^{10} - 10x^{9} - 5x^{8} + 243x^{7} - 251x^{6} - 1610x^{5} + 1411x^{4} + 3745x^{3} - 20x^{2} - 480x + 64$
579.2.a.g	$x^{13} - 8x^{12} - 32x^{11} + 397x^{10} - 228x^{9} - 5443x^{8} + 11772x^{7} + 15487x^{6} - 64085x^{5} + 34519x^{4} + 38200x^{3} - 27748x^{2} - 820x + 1228$

Dimensions

Newforms $S_{2}^{\mathrm{new}}(\Gamma_0(579))$	33
Old forms	30
Cusp forms $S_{2}(\Gamma_0(579))$	63
Eisenstein series $E_{2}(\Gamma_0(579))$	3
Modular forms $M_{2}(\Gamma_0(579))$	66

Decomposition of the old subspace

$S_{2}^{\mathrm{old}}(\Gamma_0(579)) =$ $S_{2}^{\mathrm{new}}(\Gamma_0(193))^{\oplus 2}$

Provenance

Stored in the atlas: computed by Sagebrush's modular symbols engine in 0.309 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, 193, 579]: [0, 1, 16, 66] (certified at ell = 2147483137)
T = [(2, 1), (5, 1)]; h of degree 33 = 1 x 33 (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(579, 2)

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

cargo run --release -p sagebrush-web --example atlas -- 579:2 1000

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