Atlas › Modular forms › Weight 2 › Level 683 › 683.2.a

Newspace 683.2.a: $S_{2}^{\mathrm{new}}(\Gamma_0(683))$

Newforms

Label	Dim	Coefficient field	Trace form	AL signs	Sign
683.2.a.a	2	$\mathbb{Q}(\sqrt{5})$	$2q + 3q^{3} + 6q^{4} - 2q^{5} - 5q^{6} + 4q^{7} + O(q^{8})$	−	$+1$
683.2.a.b	24	degree 24	$24q - 4q^{2} - 8q^{3} + 18q^{4} - 16q^{5} - 14q^{6} - 24q^{7} + O(q^{8})$	+	$-1$
683.2.a.c	31	degree 31	$31q + 2q^{2} + 3q^{3} + 30q^{4} + 18q^{5} + 7q^{6} + 20q^{7} + O(q^{8})$	−	$+1$

Hecke characteristic polynomials

The eigenvalue of $T = T_{2} + T_{3}$ 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 $T$
683.2.a.a	$x^{2} - 3x + 1$
683.2.a.b	$x^{24} + 12x^{23} + 8x^{22} - 387x^{21} - 1034x^{20} + 4631x^{19} + 16648x^{18} - 29536x^{17} - 121094x^{16} + 127948x^{15} + 469333x^{14} - 436933x^{13} - 958573x^{12} + 1043858x^{11} + 831319x^{10} - 1294168x^{9} - 2406x^{8} + 525520x^{7} - 132235x^{6} - 70270x^{5} + 26607x^{4} + 1787x^{3} - 1094x^{2} + 4x + 11$
683.2.a.c	$x^{31} - 5x^{30} - 104x^{29} + 532x^{28} + 4575x^{27} - 23909x^{26} - 113096x^{25} + 600227x^{24} + 1769011x^{23} - 9392808x^{22} - 18755020x^{21} + 96720526x^{20} + 141116851x^{19} - 672467224x^{18} - 775278914x^{17} + 3173240002x^{16} + 3130892456x^{15} - 10008752748x^{14} - 9089042740x^{13} + 20226436632x^{12} + 17892980899x^{11} - 23969518582x^{10} - 21456104663x^{9} + 13749264263x^{8} + 12831504056x^{7} - 2232679256x^{6} - 2478721820x^{5} - 811126x^{4} + 64562587x^{3} + 793916x^{2} - 115362x - 1931$

Dimensions

Newforms $S_{2}^{\mathrm{new}}(\Gamma_0(683))$	57
Old forms	0
Cusp forms $S_{2}(\Gamma_0(683))$	57
Eisenstein series $E_{2}(\Gamma_0(683))$	1
Modular forms $M_{2}(\Gamma_0(683))$	58

Decomposition of the old subspace

The old subspace is 0.

Provenance

Stored in the atlas: computed by Sagebrush's modular symbols engine in 0.23 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, 683]: [0, 58] (certified at ell = 2147483647)
T = [(2, 1), (3, 1)]; h of degree 57 = 1 x 57 (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(683, 2)

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

cargo run --release -p sagebrush-web --example atlas -- 683:2 1000

← 682.2.a · 684.2.a →