Atlas › Modular forms › Weight 2 › Level 983 › 983.2.a

Newspace 983.2.a: $S_{2}^{\mathrm{new}}(\Gamma_0(983))$

Newforms

Label	Dim	Coefficient field	Trace form	AL signs	Sign	CM	Elliptic curve
983.2.a.a	28	degree 28	$28q - 7q^{2} - 6q^{3} + 17q^{4} - 7q^{5} - 7q^{6} - 25q^{7} + O(q^{8})$	+	$-1$
983.2.a.b	54	degree 54	$54q + 8q^{2} + 6q^{3} + 64q^{4} + 7q^{5} + 5q^{6} + 31q^{7} + O(q^{8})$	−	$+1$

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 $T$
983.2.a.a	$x^{28} + 13x^{27} + 10x^{26} - 506x^{25} - 1555x^{24} + 7942x^{23} + 36401x^{22} - 62311x^{21} - 425126x^{20} + 223924x^{19} + 2972438x^{18} + 58930x^{17} - 13315014x^{16} - 3679775x^{15} + 39316046x^{14} + 14305818x^{13} - 76954283x^{12} - 26506612x^{11} + 97838130x^{10} + 26445907x^{9} - 76468566x^{8} - 15351570x^{7} + 33628338x^{6} + 6549460x^{5} - 7661438x^{4} - 1878865x^{3} + 669083x^{2} + 237706x + 15085$
983.2.a.b	$x^{54} - 14x^{53} - 111x^{52} + 2360x^{51} + 2697x^{50} - 179089x^{49} + 225589x^{48} + 8104785x^{47} - 21281448x^{46} - 244049827x^{45} + 891850160x^{44} + 5159234525x^{43} - 23864025223x^{42} - 78581188962x^{41} + 451379264271x^{40} + 867570562965x^{39} - 6324281642990x^{38} - 6825910521764x^{37} + 67370787677215x^{36} + 35850255940786x^{35} - 554416492643671x^{34} - 95295601131327x^{33} + 3560525262951157x^{32} - 206628357147179x^{31} - 17959537702513957x^{30} + 3405747145593989x^{29} + 71400021337438578x^{28} - 17335004273542240x^{27} - 223840006225043853x^{26} + 51876393824062711x^{25} + 551531427544872129x^{24} - 93140137214254004x^{23} - 1058914010115507790x^{22} + 70075738080758454x^{21} + 1558905418127889830x^{20} + 101159484363082524x^{19} - 1712449067749539690x^{18} - 369332153130280601x^{17} + 1340596865295621682x^{16} + 516418198587860271x^{15} - 686742556317901656x^{14} - 408525933160076552x^{13} + 186578051903695975x^{12} + 182816976227886889x^{11} - 3668011888340525x^{10} - 39074157989857628x^{9} - 9474784599070369x^{8} + 1869176801343401x^{7} + 989437488258931x^{6} + 61042445704814x^{5} - 19902464268304x^{4} - 2349593492964x^{3} + 71136808273x^{2} + 17371375388x + 533000719$

Orbit

Characteristic polynomial of

T

983.2.a.a

x^{28} + 13x^{27} + 10x^{26} - 506x^{25} - 1555x^{24} + 7942x^{23} + 36401x^{22} - 62311x^{21} - 425126x^{20} + 223924x^{19} + 2972438x^{18} + 58930x^{17} - 13315014x^{16} - 3679775x^{15} + 39316046x^{14} + 14305818x^{13} - 76954283x^{12} - 26506612x^{11} + 97838130x^{10} + 26445907x^{9} - 76468566x^{8} - 15351570x^{7} + 33628338x^{6} + 6549460x^{5} - 7661438x^{4} - 1878865x^{3} + 669083x^{2} + 237706x + 15085

983.2.a.b

x^{54} - 14x^{53} - 111x^{52} + 2360x^{51} + 2697x^{50} - 179089x^{49} + 225589x^{48} + 8104785x^{47} - 21281448x^{46} - 244049827x^{45} + 891850160x^{44} + 5159234525x^{43} - 23864025223x^{42} - 78581188962x^{41} + 451379264271x^{40} + 867570562965x^{39} - 6324281642990x^{38} - 6825910521764x^{37} + 67370787677215x^{36} + 35850255940786x^{35} - 554416492643671x^{34} - 95295601131327x^{33} + 3560525262951157x^{32} - 206628357147179x^{31} - 17959537702513957x^{30} + 3405747145593989x^{29} + 71400021337438578x^{28} - 17335004273542240x^{27} - 223840006225043853x^{26} + 51876393824062711x^{25} + 551531427544872129x^{24} - 93140137214254004x^{23} - 1058914010115507790x^{22} + 70075738080758454x^{21} + 1558905418127889830x^{20} + 101159484363082524x^{19} - 1712449067749539690x^{18} - 369332153130280601x^{17} + 1340596865295621682x^{16} + 516418198587860271x^{15} - 686742556317901656x^{14} - 408525933160076552x^{13} + 186578051903695975x^{12} + 182816976227886889x^{11} - 3668011888340525x^{10} - 39074157989857628x^{9} - 9474784599070369x^{8} + 1869176801343401x^{7} + 989437488258931x^{6} + 61042445704814x^{5} - 19902464268304x^{4} - 2349593492964x^{3} + 71136808273x^{2} + 17371375388x + 533000719

Dimensions

Newforms $S_{2}^{\mathrm{new}}(\Gamma_0(983))$	82
Old forms	0
Cusp forms $S_{2}(\Gamma_0(983))$	82
Eisenstein series $E_{2}(\Gamma_0(983))$	1
Modular forms $M_{2}(\Gamma_0(983))$	83

Decomposition of the old subspace

The old subspace is 0.

Provenance

Stored in the atlas: computed by Sagebrush's modular symbols engine in 0.308 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, 983]: [0, 83] (certified at ell = 2147475899)
T = [(2, 1), (3, 1)]; h of degree 82 = 1 x 82 (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(983, 2)

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

cargo run --release -p sagebrush-web --example atlas -- 983:2 1000

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