Atlas › Modular forms › Weight 2 › Level 547 › 547.2.a

Newspace 547.2.a: $S_{2}^{\mathrm{new}}(\Gamma_0(547))$

Newforms

Label	Dim	Coefficient field	Trace form	AL signs	Sign
547.2.a.a	2	$\mathbb{Q}(\sqrt{2})$	$2q - 2q^{2} + 2q^{4} - 4q^{6} + 4q^{7} + O(q^{8})$	+	$-1$
547.2.a.b	18	degree 18	$18q - 4q^{2} - 10q^{3} + 16q^{4} - 27q^{5} - 3q^{6} - 11q^{7} + O(q^{8})$	+	$-1$
547.2.a.c	25	degree 25	$25q + 4q^{2} + 8q^{3} + 26q^{4} + 29q^{5} + q^{6} + 5q^{7} + O(q^{8})$	−	$+1$

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 $T$
547.2.a.a	$x^{2} + 2x - 7$
547.2.a.b	$x^{18} + 34x^{17} + 255x^{16} - 3195x^{15} - 48994x^{14} + 16392x^{13} + 2781279x^{12} + 6366898x^{11} - 72100121x^{10} - 236853079x^{9} + 954118420x^{8} + 3304529852x^{7} - 6517466429x^{6} - 18660492525x^{5} + 18407238076x^{4} + 36746402496x^{3} - 8254246851x^{2} - 5051748480x - 432751568$
547.2.a.c	$x^{25} - 28x^{24} - 117x^{23} + 9929x^{22} - 43855x^{21} - 1363320x^{20} + 11770074x^{19} + 86703929x^{18} - 1218143637x^{17} - 1792974807x^{16} + 67806194283x^{15} - 90000888780x^{14} - 2165200388084x^{13} + 7027320006180x^{12} + 37744288454364x^{11} - 202435650401052x^{10} - 255100535157612x^{9} + 2943567871498945x^{8} - 1822501327101462x^{7} - 20009435452773222x^{6} + 37070568848220987x^{5} + 35012432638213166x^{4} - 140558734364355690x^{3} + 94764580560059956x^{2} + 6379192437615424x - 4100708899848448$

Dimensions

Newforms $S_{2}^{\mathrm{new}}(\Gamma_0(547))$	45
Old forms	0
Cusp forms $S_{2}(\Gamma_0(547))$	45
Eisenstein series $E_{2}(\Gamma_0(547))$	1
Modular forms $M_{2}(\Gamma_0(547))$	46

Decomposition of the old subspace

The old subspace is 0.

Provenance

Stored in the atlas: computed by Sagebrush's modular symbols engine in 0.208 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, 547]: [0, 46] (certified at ell = 2147481883)
T = [(2, 1), (3, 3)]; h of degree 45 = 1 x 45 (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(547, 2)

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

cargo run --release -p sagebrush-web --example atlas -- 547:2 1000

← 546.2.a · 548.2.a →