Atlas › Modular forms › Weight 4 › Level 227 › 227.4.a

Newspace 227.4.a: $S_{4}^{\mathrm{new}}(\Gamma_0(227))$

Newforms

Label	Dim	Coefficient field	Trace form	AL signs	Sign	CM	Elliptic curve
227.4.a.a	23	degree 23	$23q - 7q^{2} - 17q^{3} + 65q^{4} - 41q^{5} - 51q^{6} - 86q^{7} + O(q^{8})$	−	$-1$
227.4.a.b	33	degree 33	$33q + 7q^{2} + 13q^{3} + 165q^{4} + 49q^{5} + 21q^{6} + 96q^{7} + O(q^{8})$	+	$+1$

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 $T$
227.4.a.a	$x^{23} + 24x^{22} - 158x^{21} - 6995x^{20} - 918x^{19} + 850610x^{18} + 1527423x^{17} - 57416830x^{16} - 118293321x^{15} + 2369651095x^{14} + 4069892303x^{13} - 61316445425x^{12} - 69403558414x^{11} + 982562164231x^{10} + 492373863223x^{9} - 9348643930946x^{8} + 792054327783x^{7} + 48224567356511x^{6} - 28232072864650x^{5} - 107337591598653x^{4} + 106138238869372x^{3} + 32127413146550x^{2} - 43191802541404x + 1916228672804$
227.4.a.b	$x^{33} - 20x^{32} - 678x^{31} + 14993x^{30} + 188895x^{29} - 4796542x^{28} - 28364577x^{27} + 869795717x^{26} + 2540041902x^{25} - 100247306125x^{24} - 143008162630x^{23} + 7791862995958x^{22} + 5472203568515x^{21} - 421924390958862x^{20} - 182612527516801x^{19} + 16170919540638221x^{18} + 7363397201102890x^{17} - 440017904041735647x^{16} - 295763809896581842x^{15} + 8421140031441099306x^{14} + 8585927113770564095x^{13} - 110500741723726129170x^{12} - 161748791818106771743x^{11} + 941859217409384237969x^{10} + 1907879121854725244841x^{9} - 4599307175007621847013x^{8} - 13397968233192976913270x^{7} + 7885591523463543985609x^{6} + 49620733419536028847276x^{5} + 25163916982268905589726x^{4} - 65028447220428447145898x^{3} - 93961344913851903459680x^{2} - 43307004919780448080896x - 5701841631591785466048$

Orbit

Characteristic polynomial of

T

227.4.a.a

x^{23} + 24x^{22} - 158x^{21} - 6995x^{20} - 918x^{19} + 850610x^{18} + 1527423x^{17} - 57416830x^{16} - 118293321x^{15} + 2369651095x^{14} + 4069892303x^{13} - 61316445425x^{12} - 69403558414x^{11} + 982562164231x^{10} + 492373863223x^{9} - 9348643930946x^{8} + 792054327783x^{7} + 48224567356511x^{6} - 28232072864650x^{5} - 107337591598653x^{4} + 106138238869372x^{3} + 32127413146550x^{2} - 43191802541404x + 1916228672804

227.4.a.b

x^{33} - 20x^{32} - 678x^{31} + 14993x^{30} + 188895x^{29} - 4796542x^{28} - 28364577x^{27} + 869795717x^{26} + 2540041902x^{25} - 100247306125x^{24} - 143008162630x^{23} + 7791862995958x^{22} + 5472203568515x^{21} - 421924390958862x^{20} - 182612527516801x^{19} + 16170919540638221x^{18} + 7363397201102890x^{17} - 440017904041735647x^{16} - 295763809896581842x^{15} + 8421140031441099306x^{14} + 8585927113770564095x^{13} - 110500741723726129170x^{12} - 161748791818106771743x^{11} + 941859217409384237969x^{10} + 1907879121854725244841x^{9} - 4599307175007621847013x^{8} - 13397968233192976913270x^{7} + 7885591523463543985609x^{6} + 49620733419536028847276x^{5} + 25163916982268905589726x^{4} - 65028447220428447145898x^{3} - 93961344913851903459680x^{2} - 43307004919780448080896x - 5701841631591785466048

Dimensions

Newforms $S_{4}^{\mathrm{new}}(\Gamma_0(227))$	56
Old forms	0
Cusp forms $S_{4}(\Gamma_0(227))$	56
Eisenstein series $E_{4}(\Gamma_0(227))$	2
Modular forms $M_{4}(\Gamma_0(227))$	58

Decomposition of the old subspace

The old subspace is 0.

Provenance

Stored in the atlas: computed by Sagebrush's modular symbols engine in 0.155 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, 227]: [1, 58] (certified at ell = 2147479573)
T = [(2, 1), (3, 1)]; h of degree 56 = 1 x 56 (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(227, 4)

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

cargo run --release -p sagebrush-web --example atlas -- 227:4 1000

← 226.4.a · 228.4.a →