Atlas › Modular forms › Weight 4 › Level 181 › 181.4.a

Newspace 181.4.a: $S_{4}^{\mathrm{new}}(\Gamma_0(181))$

Newforms

Label	Dim	Coefficient field	Trace form	AL signs	Sign
181.4.a.a	1	$\mathbb{Q}$	$q - 3q^{2} + 7q^{3} + q^{4} - 18q^{5} - 21q^{6} + 20q^{7} + O(q^{8})$	−	$-1$
181.4.a.b	19	degree 19	$19q - 8q^{2} - 24q^{3} + 64q^{4} - 16q^{5} - 32q^{6} - 73q^{7} + O(q^{8})$	−	$-1$
181.4.a.c	25	degree 25	$25q + 7q^{2} + 19q^{3} + 125q^{4} + 26q^{5} + 31q^{6} + 31q^{7} + O(q^{8})$	+	$+1$

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 $T$
181.4.a.a	$x - 4$
181.4.a.b	$x^{19} + 32x^{18} + 161x^{17} - 4166x^{16} - 41787x^{15} + 146202x^{14} + 2585516x^{13} - 145916x^{12} - 65493470x^{11} - 53672859x^{10} + 749797939x^{9} + 536967679x^{8} - 3846317481x^{7} - 87053082x^{6} + 7754508502x^{5} - 6787159709x^{4} + 1705354273x^{3} + 94640317x^{2} - 52200870x - 2944934$
181.4.a.c	$x^{25} - 26x^{24} - 335x^{23} + 13356x^{22} + 13793x^{21} - 2761194x^{20} + 7175070x^{19} + 312123736x^{18} - 1310490834x^{17} - 21949902219x^{16} + 107909056847x^{15} + 1028594412811x^{14} - 5216991294707x^{13} - 33271575342744x^{12} + 159277395665534x^{11} + 749407470361645x^{10} - 3121876357611145x^{9} - 11554392233833243x^{8} + 38635214612499724x^{7} + 116704408862224470x^{6} - 286867673425176732x^{5} - 716308030002589104x^{4} + 1138532105646240224x^{3} + 2345117519308738016x^{2} - 1773278413614323648x - 3070578049436269312$

Dimensions

Newforms $S_{4}^{\mathrm{new}}(\Gamma_0(181))$	45
Old forms	0
Cusp forms $S_{4}(\Gamma_0(181))$	45
Eisenstein series $E_{4}(\Gamma_0(181))$	2
Modular forms $M_{4}(\Gamma_0(181))$	47

Decomposition of the old subspace

The old subspace is 0.

Provenance

Stored in the atlas: computed by Sagebrush's modular symbols engine in 0.132 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, 181]: [1, 47] (certified at ell = 2147482801)
T = [(2, 1), (3, 1)]; h of degree 45 = 1 x 45 (phi(ord eps) x dim S_k^new); 7 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(181, 4)

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

cargo run --release -p sagebrush-web --example atlas -- 181:4 1000

← 180.4.a · 182.4.a →