Atlas › Modular forms › Weight 4 › Level 233 › 233.4.a

Newspace 233.4.a: $S_{4}^{\mathrm{new}}(\Gamma_0(233))$

Newforms

Label	Dim	Coefficient field	Trace form	AL signs	Sign	CM	Elliptic curve
233.4.a.a	26	degree 26	$26q - 4q^{2} - 32q^{3} + 80q^{4} - 26q^{5} - 40q^{6} - 150q^{7} + O(q^{8})$	−	$-1$
233.4.a.b	32	degree 32	$32q + 4q^{2} + 28q^{3} + 152q^{4} + 24q^{5} + 20q^{6} + 158q^{7} + O(q^{8})$	+	$+1$

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 $T$
233.4.a.a	$x^{26} + 36x^{25} + 96x^{24} - 10222x^{23} - 93218x^{22} + 1119859x^{21} + 15392984x^{20} - 57995487x^{19} - 1245821503x^{18} + 1242831109x^{17} + 59081950470x^{16} + 7254372669x^{15} - 1758212761888x^{14} - 841191791792x^{13} + 33700482806663x^{12} + 13757901848292x^{11} - 413829703327832x^{10} - 39398320014245x^{9} + 3118334604050996x^{8} - 1057751632920477x^{7} - 12912266724440318x^{6} + 10524251871653906x^{5} + 21628165813806167x^{4} - 28912888193109198x^{3} + 1763555844275334x^{2} + 7496810254674912x - 1360496730516642$
233.4.a.b	$x^{32} - 32x^{31} - 322x^{30} + 19570x^{29} - 30177x^{28} - 4923593x^{27} + 27463024x^{26} + 680445195x^{25} - 5351457971x^{24} - 58262265578x^{23} + 554754454138x^{22} + 3328514110378x^{21} - 35854716967065x^{20} - 135073768135489x^{19} + 1536595297672331x^{18} + 4140372516879701x^{17} - 44728161405594284x^{16} - 100211489761803059x^{15} + 883363314504585705x^{14} + 1901529771039067887x^{13} - 11525963772708978702x^{12} - 26452458507385264337x^{11} + 93379997536546515131x^{10} + 243509392852657150433x^{9} - 414378824803687540298x^{8} - 1303518296268064658436x^{7} + 777652039682976213373x^{6} + 3417300894262480068400x^{5} - 560251960786837864872x^{4} - 4188850222289705061496x^{3} + 459912636308901498060x^{2} + 2041329934726067403328x - 533453661373543916192$

Orbit

Characteristic polynomial of

T

233.4.a.a

x^{26} + 36x^{25} + 96x^{24} - 10222x^{23} - 93218x^{22} + 1119859x^{21} + 15392984x^{20} - 57995487x^{19} - 1245821503x^{18} + 1242831109x^{17} + 59081950470x^{16} + 7254372669x^{15} - 1758212761888x^{14} - 841191791792x^{13} + 33700482806663x^{12} + 13757901848292x^{11} - 413829703327832x^{10} - 39398320014245x^{9} + 3118334604050996x^{8} - 1057751632920477x^{7} - 12912266724440318x^{6} + 10524251871653906x^{5} + 21628165813806167x^{4} - 28912888193109198x^{3} + 1763555844275334x^{2} + 7496810254674912x - 1360496730516642

233.4.a.b

x^{32} - 32x^{31} - 322x^{30} + 19570x^{29} - 30177x^{28} - 4923593x^{27} + 27463024x^{26} + 680445195x^{25} - 5351457971x^{24} - 58262265578x^{23} + 554754454138x^{22} + 3328514110378x^{21} - 35854716967065x^{20} - 135073768135489x^{19} + 1536595297672331x^{18} + 4140372516879701x^{17} - 44728161405594284x^{16} - 100211489761803059x^{15} + 883363314504585705x^{14} + 1901529771039067887x^{13} - 11525963772708978702x^{12} - 26452458507385264337x^{11} + 93379997536546515131x^{10} + 243509392852657150433x^{9} - 414378824803687540298x^{8} - 1303518296268064658436x^{7} + 777652039682976213373x^{6} + 3417300894262480068400x^{5} - 560251960786837864872x^{4} - 4188850222289705061496x^{3} + 459912636308901498060x^{2} + 2041329934726067403328x - 533453661373543916192

Dimensions

Newforms $S_{4}^{\mathrm{new}}(\Gamma_0(233))$	58
Old forms	0
Cusp forms $S_{4}(\Gamma_0(233))$	58
Eisenstein series $E_{4}(\Gamma_0(233))$	2
Modular forms $M_{4}(\Gamma_0(233))$	60

Decomposition of the old subspace

The old subspace is 0.

Provenance

Stored in the atlas: computed by Sagebrush's modular symbols engine in 0.159 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, 233]: [1, 60] (certified at ell = 2147482481)
T = [(2, 1), (3, 1)]; h of degree 58 = 1 x 58 (phi(ord eps) x dim S_k^new); 8 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(233, 4)

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

cargo run --release -p sagebrush-web --example atlas -- 233:4 1000

← 232.4.a · 234.4.a →