Atlas › Modular forms › Weight 2 › Level 883 › 883.2.a

Newspace 883.2.a: $S_{2}^{\mathrm{new}}(\Gamma_0(883))$

Newforms

Label	Dim	Coefficient field	Trace form	AL signs	Sign	CM	Elliptic curve
883.2.a.a	34	degree 34	$34q - 12q^{2} - 11q^{3} + 32q^{4} - 31q^{5} - 7q^{6} - 10q^{7} + O(q^{8})$	+	$-1$
883.2.a.b	39	degree 39	$39q + 10q^{2} + 7q^{3} + 40q^{4} + 29q^{5} + q^{6} + 6q^{7} + O(q^{8})$	−	$+1$

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 $T$
883.2.a.a	$x^{34} + 23x^{33} + 158x^{32} - 248x^{31} - 7691x^{30} - 21409x^{29} + 116345x^{28} + 671228x^{27} - 435559x^{26} - 8884927x^{25} - 7409337x^{24} + 66662800x^{23} + 115099584x^{22} - 306807106x^{21} - 789684792x^{20} + 859124481x^{19} + 3295805460x^{18} - 1245942160x^{17} - 9045096895x^{16} - 124423913x^{15} + 16650336808x^{14} + 4141447490x^{13} - 20356296268x^{12} - 7921397451x^{11} + 15957215007x^{10} + 7335554970x^{9} - 7514022698x^{8} - 3490291916x^{7} + 1907884166x^{6} + 752218553x^{5} - 216178720x^{4} - 57515162x^{3} + 4778720x^{2} + 1510472x + 72575$
883.2.a.b	$x^{39} - 17x^{38} + 5x^{37} + 1449x^{36} - 6259x^{35} - 46505x^{34} + 348116x^{33} + 567429x^{32} - 9248558x^{31} + 4061831x^{30} + 143884438x^{29} - 232571441x^{28} - 1400298875x^{27} + 3573644372x^{26} + 8659597980x^{25} - 31231778871x^{24} - 33143698872x^{23} + 176890239533x^{22} + 69248388465x^{21} - 685278976267x^{20} - 24584330025x^{19} + 1869682604207x^{18} - 269892681284x^{17} - 3646425019621x^{16} + 782760569651x^{15} + 5094324732701x^{14} - 1096159092829x^{13} - 5043505680096x^{12} + 892099260886x^{11} + 3458098683647x^{10} - 431332365586x^{9} - 1587993501599x^{8} + 119547367736x^{7} + 465920630566x^{6} - 17338920611x^{5} - 81318309328x^{4} + 1122282473x^{3} + 7452433768x^{2} - 24350032x - 264894784$

Orbit

Characteristic polynomial of

T

883.2.a.a

x^{34} + 23x^{33} + 158x^{32} - 248x^{31} - 7691x^{30} - 21409x^{29} + 116345x^{28} + 671228x^{27} - 435559x^{26} - 8884927x^{25} - 7409337x^{24} + 66662800x^{23} + 115099584x^{22} - 306807106x^{21} - 789684792x^{20} + 859124481x^{19} + 3295805460x^{18} - 1245942160x^{17} - 9045096895x^{16} - 124423913x^{15} + 16650336808x^{14} + 4141447490x^{13} - 20356296268x^{12} - 7921397451x^{11} + 15957215007x^{10} + 7335554970x^{9} - 7514022698x^{8} - 3490291916x^{7} + 1907884166x^{6} + 752218553x^{5} - 216178720x^{4} - 57515162x^{3} + 4778720x^{2} + 1510472x + 72575

883.2.a.b

x^{39} - 17x^{38} + 5x^{37} + 1449x^{36} - 6259x^{35} - 46505x^{34} + 348116x^{33} + 567429x^{32} - 9248558x^{31} + 4061831x^{30} + 143884438x^{29} - 232571441x^{28} - 1400298875x^{27} + 3573644372x^{26} + 8659597980x^{25} - 31231778871x^{24} - 33143698872x^{23} + 176890239533x^{22} + 69248388465x^{21} - 685278976267x^{20} - 24584330025x^{19} + 1869682604207x^{18} - 269892681284x^{17} - 3646425019621x^{16} + 782760569651x^{15} + 5094324732701x^{14} - 1096159092829x^{13} - 5043505680096x^{12} + 892099260886x^{11} + 3458098683647x^{10} - 431332365586x^{9} - 1587993501599x^{8} + 119547367736x^{7} + 465920630566x^{6} - 17338920611x^{5} - 81318309328x^{4} + 1122282473x^{3} + 7452433768x^{2} - 24350032x - 264894784

Dimensions

Newforms $S_{2}^{\mathrm{new}}(\Gamma_0(883))$	73
Old forms	0
Cusp forms $S_{2}(\Gamma_0(883))$	73
Eisenstein series $E_{2}(\Gamma_0(883))$	1
Modular forms $M_{2}(\Gamma_0(883))$	74

Decomposition of the old subspace

The old subspace is 0.

Provenance

Stored in the atlas: computed by Sagebrush's modular symbols engine in 0.292 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, 883]: [0, 74] (certified at ell = 2147479489)
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(883, 2)

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

cargo run --release -p sagebrush-web --example atlas -- 883:2 1000

← 882.2.a · 884.2.a →