Atlas › Modular forms › Weight 2 › Level 583 › 583.2.a

Newspace 583.2.a: $S_{2}^{\mathrm{new}}(\Gamma_0(583))$

Newforms

Label	Dim	Coefficient field	Trace form	AL signs	Sign	Elliptic curve
583.2.a.a	1	$\mathbb{Q}$	$q + q^{2} - q^{3} - q^{4} + 4q^{5} - q^{6} + 4q^{7} + O(q^{8})$	− +	$+1$	583b1 rank 0
583.2.a.b	1	$\mathbb{Q}$	$q + 2q^{2} + q^{3} + 2q^{4} + 3q^{5} + 2q^{6} + O(q^{8})$	+ −	$+1$	583a1 rank 0
583.2.a.c	1	$\mathbb{Q}$	$q + 2q^{2} + 3q^{3} + 2q^{4} - 3q^{5} + 6q^{6} + 2q^{7} + O(q^{8})$	− +	$+1$	583c1 rank 0
583.2.a.d	2	$\mathbb{Q}(\sqrt{3})$	$2q - 2q^{2} + 4q^{4} + 6q^{6} - 2q^{7} + O(q^{8})$	+ +	$-1$
583.2.a.e	2	$\mathbb{Q}(\sqrt{2})$	$2q - 2q^{3} - 6q^{5} + 4q^{6} + 4q^{7} + O(q^{8})$	+ +	$-1$
583.2.a.f	6	degree 6	$6q - 2q^{2} + 2q^{3} + 8q^{4} - 3q^{5} - 20q^{6} - 11q^{7} + O(q^{8})$	+ +	$-1$
583.2.a.g	8	degree 8	$8q - 2q^{2} - 8q^{3} + 6q^{4} - 11q^{5} + 2q^{6} - q^{7} + O(q^{8})$	− −	$-1$
583.2.a.h	10	degree 10	$10q + 3q^{2} - q^{3} + 9q^{4} + 8q^{5} - 2q^{6} + 3q^{7} + O(q^{8})$	+ −	$+1$
583.2.a.i	12	degree 12	$12q + q^{2} + 6q^{3} + 15q^{4} + 10q^{5} - 5q^{6} - 3q^{7} + O(q^{8})$	− +	$+1$

Hecke characteristic polynomials

The eigenvalue of $T = T_{2} + 3T_{3}$ 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 $T$
583.2.a.a	$x + 2$
583.2.a.b	$x - 5$
583.2.a.c	$x - 11$
583.2.a.d	$x^{2} + 2x - 47$
583.2.a.e	$x^{2} + 6x - 23$
583.2.a.f	$x^{6} - 4x^{5} - 32x^{4} + 128x^{3} + 160x^{2} - 640x - 64$
583.2.a.g	$x^{8} + 26x^{7} + 186x^{6} - 176x^{5} - 5567x^{4} - 9738x^{3} + 25796x^{2} + 41512x - 12944$
583.2.a.h	$x^{10} - 211x^{8} - 102x^{7} + 15853x^{6} + 11230x^{5} - 509471x^{4} - 334360x^{3} + 6695972x^{2} + 2426144x - 29269232$
583.2.a.i	$x^{12} - 19x^{11} - 67x^{10} + 3287x^{9} - 12767x^{8} - 131783x^{7} + 958409x^{6} + 668419x^{5} - 18838176x^{4} + 32891720x^{3} + 73559312x^{2} - 233399840x + 129189216$

Dimensions

Newforms $S_{2}^{\mathrm{new}}(\Gamma_0(583))$	43
Old forms	10
Cusp forms $S_{2}(\Gamma_0(583))$	53
Eisenstein series $E_{2}(\Gamma_0(583))$	3
Modular forms $M_{2}(\Gamma_0(583))$	56

Decomposition of the old subspace

$S_{2}^{\mathrm{old}}(\Gamma_0(583)) =$ $S_{2}^{\mathrm{new}}(\Gamma_0(11))^{\oplus 2}$ $\oplus$ $S_{2}^{\mathrm{new}}(\Gamma_0(53))^{\oplus 2}$

Provenance

Stored in the atlas: computed by Sagebrush's modular symbols engine in 0.221 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, 11, 53, 583]: [0, 2, 5, 56] (certified at ell = 2147482481)
T = [(2, 1), (3, 3)]; h of degree 43 = 1 x 43 (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(583, 2)

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

cargo run --release -p sagebrush-web --example atlas -- 583:2 1000

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