Atlas › Modular forms › Weight 2 › Level 653 › 653.2.a

Newspace 653.2.a: $S_{2}^{\mathrm{new}}(\Gamma_0(653))$

Newforms

Label	Dim	Coefficient field	Trace form	AL signs	Sign
653.2.a.a	7	degree 7	$7q - 9q^{3} + 2q^{4} + 5q^{5} + 4q^{6} - 16q^{7} + O(q^{8})$	+	$-1$
653.2.a.b	17	degree 17	$17q - 4q^{2} - 10q^{3} + 16q^{4} - 10q^{5} - 12q^{6} - 9q^{7} + O(q^{8})$	+	$-1$
653.2.a.c	30	degree 30	$30q + 2q^{2} + 19q^{3} + 32q^{4} + q^{5} + 2q^{6} + 23q^{7} + O(q^{8})$	−	$+1$

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 $T$
653.2.a.a	$x^{7} + 9x^{6} + 16x^{5} - 48x^{4} - 127x^{3} + 62x^{2} + 193x - 29$
653.2.a.b	$x^{17} + 14x^{16} + 49x^{15} - 123x^{14} - 954x^{13} - 461x^{12} + 5305x^{11} + 6997x^{10} - 10252x^{9} - 21889x^{8} - 194x^{7} + 21714x^{6} + 14832x^{5} + 808x^{4} - 2612x^{3} - 1046x^{2} - 151x - 7$
653.2.a.c	$x^{30} - 21x^{29} + 111x^{28} + 626x^{27} - 8157x^{26} + 10642x^{25} + 175958x^{24} - 673049x^{23} - 1353543x^{22} + 11320243x^{21} - 4002569x^{20} - 93149673x^{19} + 144171090x^{18} + 394043027x^{17} - 1081061924x^{16} - 652872229x^{15} + 4014231609x^{14} - 951851945x^{13} - 7958282394x^{12} + 5718949288x^{11} + 7972620418x^{10} - 9023129280x^{9} - 3154243854x^{8} + 6209477072x^{7} - 268301183x^{6} - 1755092961x^{5} + 366755152x^{4} + 152159901x^{3} - 38861416x^{2} - 1649586x + 190689$

Dimensions

Newforms $S_{2}^{\mathrm{new}}(\Gamma_0(653))$	54
Old forms	0
Cusp forms $S_{2}(\Gamma_0(653))$	54
Eisenstein series $E_{2}(\Gamma_0(653))$	1
Modular forms $M_{2}(\Gamma_0(653))$	55

Decomposition of the old subspace

The old subspace is 0.

Provenance

Stored in the atlas: computed by Sagebrush's modular symbols engine in 0.219 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, 653]: [0, 55] (certified at ell = 2147482621)
T = [(2, 1), (3, 1)]; h of degree 54 = 1 x 54 (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(653, 2)

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

cargo run --release -p sagebrush-web --example atlas -- 653:2 1000

← 652.2.a · 654.2.a →