Atlas › Modular forms › Weight 2 › Level 881 › 881.2.a

Newspace 881.2.a: $S_{2}^{\mathrm{new}}(\Gamma_0(881))$

Newforms

Label	Dim	Coefficient field	Trace form	AL signs	Sign	CM	Elliptic curve
881.2.a.a	27	degree 27	$27q - 5q^{2} - 9q^{3} + 11q^{4} - 6q^{5} - 5q^{6} - 27q^{7} + O(q^{8})$	+	$-1$
881.2.a.b	46	degree 46	$46q + 4q^{2} + 7q^{3} + 64q^{4} + 5q^{6} + 31q^{7} + O(q^{8})$	−	$+1$

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 $T$
881.2.a.a	$x^{27} + 14x^{26} + 25x^{25} - 476x^{24} - 2087x^{23} + 5466x^{22} + 42262x^{21} - 11954x^{20} - 424830x^{19} - 267903x^{18} + 2465291x^{17} + 2693838x^{16} - 8779983x^{15} - 11651306x^{14} + 19826505x^{13} + 27244341x^{12} - 29067872x^{11} - 34830382x^{10} + 27868388x^{9} + 22061548x^{8} - 16072488x^{7} - 5180310x^{6} + 3903688x^{5} + 338283x^{4} - 302033x^{3} - 12616x^{2} + 7246x + 331$
881.2.a.b	$x^{46} - 11x^{45} - 120x^{44} + 1686x^{43} + 5286x^{42} - 115018x^{41} - 63205x^{40} + 4637379x^{39} - 3455743x^{38} - 123837396x^{37} + 189221576x^{36} + 2327878086x^{35} - 4787631423x^{34} - 31977272980x^{33} + 77945820511x^{32} + 329102630684x^{31} - 894059846185x^{30} - 2582974094276x^{29} + 7513129274147x^{28} + 15667017946936x^{27} - 47126703963819x^{26} - 74209963900642x^{25} + 222276890368033x^{24} + 276662429815853x^{23} - 787715469635410x^{22} - 814912891864653x^{21} + 2080881888443241x^{20} + 1889843003739534x^{19} - 4034819570409444x^{18} - 3398648446036471x^{17} + 5604766587637319x^{16} + 4598841837584354x^{15} - 5385430926426912x^{14} - 4472865456791658x^{13} + 3416140415213301x^{12} + 2950151049336420x^{11} - 1358066796679579x^{10} - 1241965167746681x^{9} + 326210898146953x^{8} + 318829608744981x^{7} - 46089674878804x^{6} - 47229945694618x^{5} + 3900688213958x^{4} + 3625527372656x^{3} - 235070917653x^{2} - 109157340571x + 9760252369$

Orbit

Characteristic polynomial of

T

881.2.a.a

x^{27} + 14x^{26} + 25x^{25} - 476x^{24} - 2087x^{23} + 5466x^{22} + 42262x^{21} - 11954x^{20} - 424830x^{19} - 267903x^{18} + 2465291x^{17} + 2693838x^{16} - 8779983x^{15} - 11651306x^{14} + 19826505x^{13} + 27244341x^{12} - 29067872x^{11} - 34830382x^{10} + 27868388x^{9} + 22061548x^{8} - 16072488x^{7} - 5180310x^{6} + 3903688x^{5} + 338283x^{4} - 302033x^{3} - 12616x^{2} + 7246x + 331

881.2.a.b

x^{46} - 11x^{45} - 120x^{44} + 1686x^{43} + 5286x^{42} - 115018x^{41} - 63205x^{40} + 4637379x^{39} - 3455743x^{38} - 123837396x^{37} + 189221576x^{36} + 2327878086x^{35} - 4787631423x^{34} - 31977272980x^{33} + 77945820511x^{32} + 329102630684x^{31} - 894059846185x^{30} - 2582974094276x^{29} + 7513129274147x^{28} + 15667017946936x^{27} - 47126703963819x^{26} - 74209963900642x^{25} + 222276890368033x^{24} + 276662429815853x^{23} - 787715469635410x^{22} - 814912891864653x^{21} + 2080881888443241x^{20} + 1889843003739534x^{19} - 4034819570409444x^{18} - 3398648446036471x^{17} + 5604766587637319x^{16} + 4598841837584354x^{15} - 5385430926426912x^{14} - 4472865456791658x^{13} + 3416140415213301x^{12} + 2950151049336420x^{11} - 1358066796679579x^{10} - 1241965167746681x^{9} + 326210898146953x^{8} + 318829608744981x^{7} - 46089674878804x^{6} - 47229945694618x^{5} + 3900688213958x^{4} + 3625527372656x^{3} - 235070917653x^{2} - 109157340571x + 9760252369

Dimensions

Newforms $S_{2}^{\mathrm{new}}(\Gamma_0(881))$	73
Old forms	0
Cusp forms $S_{2}(\Gamma_0(881))$	73
Eisenstein series $E_{2}(\Gamma_0(881))$	1
Modular forms $M_{2}(\Gamma_0(881))$	74

Decomposition of the old subspace

The old subspace is 0.

Provenance

Stored in the atlas: computed by Sagebrush's modular symbols engine in 0.28 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, 881]: [0, 74] (certified at ell = 2147482481)
T = [(2, 1), (3, 1)]; h of degree 73 = 1 x 73 (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(881, 2)

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

cargo run --release -p sagebrush-web --example atlas -- 881:2 1000

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