Atlas › Modular forms › Weight 4 › Level 173 › 173.4.a

Newspace 173.4.a: $S_{4}^{\mathrm{new}}(\Gamma_0(173))$

Newforms

Label	Dim	Coefficient field	Trace form	AL signs	Sign	CM	Elliptic curve
173.4.a.a	18	degree 18	$18q - 7q^{2} - 28q^{3} + 49q^{4} - 25q^{5} - 12q^{6} - 93q^{7} + O(q^{8})$	−	$-1$
173.4.a.b	25	degree 25	$25q + 3q^{2} + 26q^{3} + 133q^{4} + 15q^{5} + 24q^{6} + 103q^{7} + O(q^{8})$	+	$+1$

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 $T$
173.4.a.a	$x^{18} + 35x^{17} + 228x^{16} - 4365x^{15} - 54005x^{14} + 118631x^{13} + 3342910x^{12} + 2248916x^{11} - 91443107x^{10} - 142450047x^{9} + 1229512402x^{8} + 2123210348x^{7} - 7696323522x^{6} - 11074233170x^{5} + 16551707926x^{4} + 9567556858x^{3} - 4037633625x^{2} - 433550994x + 104998656$
173.4.a.b	$x^{25} - 29x^{24} - 259x^{23} + 14290x^{22} - 18751x^{21} - 2925736x^{20} + 14540710x^{19} + 326326088x^{18} - 2335503283x^{17} - 21810686966x^{16} + 196485848316x^{15} + 901290971370x^{14} - 10014849795776x^{13} - 22768372601518x^{12} + 322936873654407x^{11} + 331987362294921x^{10} - 6590537546526749x^{9} - 2490145600089452x^{8} + 82333206073222035x^{7} + 10335659358163956x^{6} - 581272065486111806x^{5} - 96425316242932604x^{4} + 1907207944319673531x^{3} + 749441085717784104x^{2} - 1292569389284967084x - 665869250741185568$

Orbit

Characteristic polynomial of

T

173.4.a.a

x^{18} + 35x^{17} + 228x^{16} - 4365x^{15} - 54005x^{14} + 118631x^{13} + 3342910x^{12} + 2248916x^{11} - 91443107x^{10} - 142450047x^{9} + 1229512402x^{8} + 2123210348x^{7} - 7696323522x^{6} - 11074233170x^{5} + 16551707926x^{4} + 9567556858x^{3} - 4037633625x^{2} - 433550994x + 104998656

173.4.a.b

x^{25} - 29x^{24} - 259x^{23} + 14290x^{22} - 18751x^{21} - 2925736x^{20} + 14540710x^{19} + 326326088x^{18} - 2335503283x^{17} - 21810686966x^{16} + 196485848316x^{15} + 901290971370x^{14} - 10014849795776x^{13} - 22768372601518x^{12} + 322936873654407x^{11} + 331987362294921x^{10} - 6590537546526749x^{9} - 2490145600089452x^{8} + 82333206073222035x^{7} + 10335659358163956x^{6} - 581272065486111806x^{5} - 96425316242932604x^{4} + 1907207944319673531x^{3} + 749441085717784104x^{2} - 1292569389284967084x - 665869250741185568

Dimensions

Newforms $S_{4}^{\mathrm{new}}(\Gamma_0(173))$	43
Old forms	0
Cusp forms $S_{4}(\Gamma_0(173))$	43
Eisenstein series $E_{4}(\Gamma_0(173))$	2
Modular forms $M_{4}(\Gamma_0(173))$	45

Decomposition of the old subspace

The old subspace is 0.

Provenance

Stored in the atlas: computed by Sagebrush's modular symbols engine in 0.125 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, 173]: [1, 45] (certified at ell = 2147482093)
T = [(2, 1), (3, 1)]; 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(173, 4)

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

cargo run --release -p sagebrush-web --example atlas -- 173:4 1000

← 172.4.a · 174.4.a →