Atlas › Modular forms › Weight 4 › Level 151 › 151.4.a

Newspace 151.4.a: $S_{4}^{\mathrm{new}}(\Gamma_0(151))$

Newforms

Label	Dim	Coefficient field	Trace form	AL signs	Sign	CM	Elliptic curve
151.4.a.a	15	degree 15	$15q - 6q^{2} - 10q^{3} + 44q^{4} - 61q^{5} - 36q^{6} - 26q^{7} + O(q^{8})$	−	$-1$
151.4.a.b	22	degree 22	$22q + 6q^{2} + 8q^{3} + 100q^{4} + 59q^{5} + 48q^{6} + 30q^{7} + O(q^{8})$	+	$+1$

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 $T$
151.4.a.a	$x^{15} + 16x^{14} - 128x^{13} - 2593x^{12} + 3884x^{11} + 130533x^{10} - 33487x^{9} - 2593052x^{8} + 263152x^{7} + 22644508x^{6} - 4315514x^{5} - 78265780x^{4} + 19548092x^{3} + 58849912x^{2} + 8169600x - 3781600$
151.4.a.b	$x^{22} - 14x^{21} - 550x^{20} + 7775x^{19} + 121884x^{18} - 1704187x^{17} - 14995995x^{16} + 198234727x^{15} + 1171912322x^{14} - 13622784462x^{13} - 62008140723x^{12} + 576247397266x^{11} + 2254637430557x^{10} - 15070026017873x^{9} - 55032035299736x^{8} + 237694354846122x^{7} + 857433194268028x^{6} - 2128562205760434x^{5} - 7903527758972180x^{4} + 9447245633001024x^{3} + 37727290344398272x^{2} - 14288741498091520x - 67372030867991488$

Orbit

Characteristic polynomial of

T

151.4.a.a

x^{15} + 16x^{14} - 128x^{13} - 2593x^{12} + 3884x^{11} + 130533x^{10} - 33487x^{9} - 2593052x^{8} + 263152x^{7} + 22644508x^{6} - 4315514x^{5} - 78265780x^{4} + 19548092x^{3} + 58849912x^{2} + 8169600x - 3781600

151.4.a.b

x^{22} - 14x^{21} - 550x^{20} + 7775x^{19} + 121884x^{18} - 1704187x^{17} - 14995995x^{16} + 198234727x^{15} + 1171912322x^{14} - 13622784462x^{13} - 62008140723x^{12} + 576247397266x^{11} + 2254637430557x^{10} - 15070026017873x^{9} - 55032035299736x^{8} + 237694354846122x^{7} + 857433194268028x^{6} - 2128562205760434x^{5} - 7903527758972180x^{4} + 9447245633001024x^{3} + 37727290344398272x^{2} - 14288741498091520x - 67372030867991488

Dimensions

Newforms $S_{4}^{\mathrm{new}}(\Gamma_0(151))$	37
Old forms	0
Cusp forms $S_{4}(\Gamma_0(151))$	37
Eisenstein series $E_{4}(\Gamma_0(151))$	2
Modular forms $M_{4}(\Gamma_0(151))$	39

Decomposition of the old subspace

The old subspace is 0.

Provenance

Stored in the atlas: computed by Sagebrush's modular symbols engine in 0.117 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, 151]: [1, 39] (certified at ell = 2147482951)
T = [(2, 1), (3, 1)]; h of degree 37 = 1 x 37 (phi(ord eps) x dim S_k^new); 5 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(151, 4)

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

cargo run --release -p sagebrush-web --example atlas -- 151:4 1000

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