Atlas › Modular forms › Weight 4 › Level 179 › 179.4.a

Newspace 179.4.a: $S_{4}^{\mathrm{new}}(\Gamma_0(179))$

Newforms

Label	Dim	Coefficient field	Trace form	AL signs	Sign	CM	Elliptic curve
179.4.a.a	17	degree 17	$17q - 2q^{2} - 9q^{3} + 30q^{4} - 45q^{5} - 46q^{6} - 44q^{7} + O(q^{8})$	−	$-1$
179.4.a.b	27	degree 27	$27q + 4q^{2} + 9q^{3} + 130q^{4} + 35q^{5} + 50q^{6} + 68q^{7} + O(q^{8})$	+	$+1$

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 $T$
179.4.a.a	$x^{17} + 11x^{16} - 240x^{15} - 2374x^{14} + 22642x^{13} + 182879x^{12} - 1127218x^{11} - 6263634x^{10} + 31299768x^{9} + 93255228x^{8} - 433371096x^{7} - 477100726x^{6} + 2245936345x^{5} + 665713679x^{4} - 3314178560x^{3} + 1385196050x^{2} - 15251250x - 6890625$
179.4.a.b	$x^{27} - 13x^{26} - 672x^{25} + 8790x^{24} + 188321x^{23} - 2435314x^{22} - 29794744x^{21} + 369207014x^{20} + 3030845625x^{19} - 34200815454x^{18} - 213154547348x^{17} + 2034521739876x^{16} + 10741612837805x^{15} - 79011158835486x^{14} - 388258532942824x^{13} + 1979172839514176x^{12} + 9776225098378369x^{11} - 30514917055488630x^{10} - 162546476683702914x^{9} + 259764918589708682x^{8} + 1649072399583355001x^{7} - 898413000353759370x^{6} - 9050320671917762982x^{5} - 795358445455265892x^{4} + 21472782517130062356x^{3} + 6603278691636885427x^{2} - 13646401920029642786x - 2791607129110945302$

Orbit

Characteristic polynomial of

T

179.4.a.a

x^{17} + 11x^{16} - 240x^{15} - 2374x^{14} + 22642x^{13} + 182879x^{12} - 1127218x^{11} - 6263634x^{10} + 31299768x^{9} + 93255228x^{8} - 433371096x^{7} - 477100726x^{6} + 2245936345x^{5} + 665713679x^{4} - 3314178560x^{3} + 1385196050x^{2} - 15251250x - 6890625

179.4.a.b

x^{27} - 13x^{26} - 672x^{25} + 8790x^{24} + 188321x^{23} - 2435314x^{22} - 29794744x^{21} + 369207014x^{20} + 3030845625x^{19} - 34200815454x^{18} - 213154547348x^{17} + 2034521739876x^{16} + 10741612837805x^{15} - 79011158835486x^{14} - 388258532942824x^{13} + 1979172839514176x^{12} + 9776225098378369x^{11} - 30514917055488630x^{10} - 162546476683702914x^{9} + 259764918589708682x^{8} + 1649072399583355001x^{7} - 898413000353759370x^{6} - 9050320671917762982x^{5} - 795358445455265892x^{4} + 21472782517130062356x^{3} + 6603278691636885427x^{2} - 13646401920029642786x - 2791607129110945302

Dimensions

Newforms $S_{4}^{\mathrm{new}}(\Gamma_0(179))$	44
Old forms	0
Cusp forms $S_{4}(\Gamma_0(179))$	44
Eisenstein series $E_{4}(\Gamma_0(179))$	2
Modular forms $M_{4}(\Gamma_0(179))$	46

Decomposition of the old subspace

The old subspace is 0.

Provenance

Stored in the atlas: computed by Sagebrush's modular symbols engine in 0.128 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, 179]: [1, 46] (certified at ell = 2147483137)
T = [(2, 1), (3, 1)]; h of degree 44 = 1 x 44 (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(179, 4)

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

cargo run --release -p sagebrush-web --example atlas -- 179:4 1000

← 178.4.a · 180.4.a →