LMFDB - Newform orbit 23.29.b.a

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [23,29,Mod(22,23)]

mf = mfinit([N,k,chi],0)

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(23, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([1]))

N = Newforms(chi, 29, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("23.22");

S:= CuspForms(chi, 29);

N := Newforms(S);

Level:	$N$	$=$	$23$
Weight:	$k$	$=$	$29$
Character orbit:	$[\chi]$	$=$	23.b (of order $2$ , degree $1$ , minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	yes
Analytic conductor:	$114.237490771$
Analytic rank:	$0$
Dimension:	$3$
Coefficient field:	3.3.621.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$x^{3} - 6x - 3$ x^3 - 6*x - 3
Coefficient ring:	$\Z[a_1, \ldots, a_{29}]$
Coefficient ring index:	$1$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{U}(1)[D_{2}]$

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/23\mathbb{Z}\right)^\times$ .

$n$	$5$
$\chi(n)$	$-1$

Embeddings

For each embedding $\iota_m$ of the coefficient field, the values $\iota_m(a_n)$ are shown below.

For more information on an embedded modular form you can click on its label.

comment: embeddings in the coefficient field

gp: mfembed(f)

Label

\iota_m(\nu)

a_{2}

a_{3}

a_{4}

a_{5}

a_{6}

a_{7}

a_{8}

a_{9}

a_{10}

22.1

2.66908
−0.523976
−2.14510

−32762.2

−8.17511e6

8.04929e8

2.67835e11

−1.75767e13

4.39556e13

22.2

15849.1

−214311.

−1.72417e7

−3.39664e9

−4.52772e12

−2.28309e13

22.3

16913.1

8.38942e6

1.76191e7

1.41892e11

−4.24209e12

4.75056e13

Inner twists

Char	Parity	Ord	Mult	Type
1.a	even	1	1	trivial
23.b	odd	2	1	CM by $\Q(\sqrt{-23})$

Twists

By twisting character orbit
Char	Parity	Ord	Mult	Type	Twist	Min	Dim
1.a	even	1	1	trivial	23.29.b.a	✓	3
23.b	odd	2	1	CM	23.29.b.a	✓	3

By twisted newform orbit
Twist	Min	Dim	Char	Parity	Ord	Mult	Type
23.29.b.a	✓	3	1.a	even	1	1	trivial
23.29.b.a	✓	3	23.b	odd	2	1	CM

This newform subspace can be constructed as the kernel of the linear operator $T_{2}^{3} - 805306368T_{2} + 8782182470959$ T2^3 - 805306368*T2 + 8782182470959 acting on $S_{29}^{\mathrm{new}}(23, [\chi])$ .

Hecke characteristic polynomials

$p$	$F_p(T)$
$2$	$T^{3} + \cdots + 8782182470959$ T^3 - 805306368*T + 8782182470959
$3$	$T^{3} + \cdots - 14\!\cdots\!46$ T^3 - 68630377364883*T - 14698426446679116946
$5$	$T^{3}$ T^3
$7$	$T^{3}$ T^3
$11$	$T^{3}$ T^3
$13$	$T^{3} + \cdots - 11\!\cdots\!86$ T^3 - 46508798407987188645808605316563*T - 115025322800064642989516070416624186354014885586
$17$	$T^{3}$ T^3
$19$	$T^{3}$ T^3
$23$	$(T - 11\!\cdots\!09)^{3}$ (T - 11592836324538749809)^3
$29$	$T^{3} + \cdots - 52\!\cdots\!74$ T^3 - 265622705499435634609844298075622357912083*T - 52295162226356720122553147400995770197412470149601107496717074
$31$	$T^{3} + \cdots + 60\!\cdots\!66$ T^3 - 1718892363202635288370042264011880912629123*T + 601280683772454271915782820215008926463473002421107582192912766
$37$	$T^{3}$ T^3
$41$	$T^{3} + \cdots - 22\!\cdots\!74$ T^3 - 4315878826810565967810301146758047455414809763*T - 22014061730232051656115535226487494221499308972254293798026165843874
$43$	$T^{3}$ T^3
$47$	$T^{3} + \cdots + 16\!\cdots\!14$ T^3 - 197633825395980758051341714229824826614933884483*T + 16706130291702140381366633581436601913349734239065558414819247401198014
$53$	$T^{3}$ T^3
$59$	$(T - 12\!\cdots\!54)^{3}$ (T - 12380695658241029459246354)^3
$61$	$T^{3}$ T^3
$67$	$T^{3}$ T^3
$71$	$T^{3} + \cdots - 52\!\cdots\!74$ T^3 - 20528396096822816945442734438199438456029111658816483*T - 522617980440838685284798998875007115048848784604961503935355742356756421423074
$73$	$T^{3} + \cdots - 16\!\cdots\!46$ T^3 - 44684956355885825831539759672432152515683464323031843*T - 1693463515575012419293447780727118055513020271836618771538955500349694102426146
$79$	$T^{3}$ T^3
$83$	$T^{3}$ T^3
$89$	$T^{3}$ T^3
$97$	$T^{3}$ T^3
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Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

$f(q)$	$=$	$q + ( - 3026 \beta_{2} - 11759 \beta_1) q^{2} + (584543 \beta_{2} - 3162522 \beta_1) q^{3} + (57951937 \beta_{2} + 191126197 \beta_1 + 268435456) q^{4} + (36260772881 \beta_{2} + \cdots + 135443271649) q^{6}+ \cdots + ( - 13\!\cdots\!26 \beta_{2} - 54\!\cdots\!59 \beta_1) q^{98}+O(q^{100})$ q + (-3026b2 - 11759b1) * q^2 + (584543b2 - 3162522b1) * q^3 + (57951937b2 + 191126197b1 + 268435456) * q^4 + (36260772881b2 + 43421900869b1 + 135443271649) * q^6 + (-812285689856b2 - 3156532527104b1 - 8782182470959) * q^8 + (13357115076527b2 + 5620904167894b1 + 22876792454961) * q^9 + (-409851340009874b2 - 1592677431320591b1 - 2142958021364447) * q^12 + (1703854593146863b2 - 1465657539771674b1) * q^13 + (26574884157121934b2 + 103269683676006881b1 + 72057594037927936) * q^16 + (79172416339521407b2 - 428342326341938778b1 - 332821457573558159) * q^18 + 11592836324538749809 * q^23 + (4600113815101881999b2 + 39429823032579009862b1 + 36357776387231186944) * q^24 + 37252902984619140625 * q^25 + (37991077454502398497b2 + 11945848562435052949b1 + 53604030492990890129) * q^26 + (13372468892000267823b2 - 72348359428248171642b1 + 14698426446679116946) * q^27 + (64801437274358585791b2 + 211735683875023885414b1) * q^29 + (-190808378063522644769b2 + 436184043584939783734b1) * q^31 + (-508944485279520297583b2 - 1678505137034456612923b1 - 2357449156267085922304) * q^32 + (2332872165729562198591b2 + 8286001861082460104998b1 + 12203937620519991681985) * q^36 + (9884415429450704366687b2 - 3601995827788656578858b1 + 30761771999525013542434) * q^39 + (5621683973994914503807b2 - 24553842284096825399018b1) * q^41 + (-35079922718054256922034b2 - 136320162340251159004031b1) * q^46 + (149317107123447458594863b2 + 7512367404809936154166b1) * q^47 + (-276327961787231167769631b2 - 609222783079467101377963b1 - 1189487526085185890541391) * q^48 + 459986536544739960976801 * q^49 + (-112727284431457519531250b2 - 438056886196136474609375b1) * q^50 + (-162205796271790433530354b2 - 630329794567079877026911b1 - 768765717709218523470799) * q^52 + (785052737027464234834045b2 + 820515017593503953093095b1 + 3098507614935076320700689) * q^54 + (-890998477179191900400527b2 - 3500333888616992594955227b1 - 9733022241583873070375167) * q^58 + 12380695658241029459246354 * q^59 + (-6630297122296461434258687b2 - 5360037670794810968810507b1 - 17975858563700845523546047) * q^62 + (7133641146864202000891904b2 + 27721244628544663360372736b1 + 57783915839385460083080865) * q^64 + (6776511323654854429602287b2 - 36662599918752936123458298b1) * q^69 + (-41592010803253273623817553b2 - 40970453790800935225828586b1) * q^71 + (-96051938204936321530272801b2 - 164346073749918218511703114b1 - 290249245420068340651663103) * q^72 + (-1786509881621186103983201b2 + 85825643716474885140040726b1) * q^73 + (21775923669338226318359375b2 - 117813125252723693847656250b1) * q^75 + (84512189617944310985228925b2 - 364882527484434516547748585b1 + 95293230878782620201843841) * q^78 + (8591862290421151056965678b2 - 46484097003004534282297812b1 + 523347633027360537213511521) * q^81 + (297545302222532387148410689b2 + 330945607730782586451254581b1 + 1044652686541455817729928801) * q^82 + (-626330625836052702559913521b2 - 826544570689560046176680234b1 - 2370032315314819831303476254) * q^87 + (671827320330981182989930033b2 + 2215694719152549030128646373b1 + 3111928305110923294648827904) * q^92 + (-2126309954947424434976182561b2 - 297966207610080282468235034b1 - 7045384768775117260566672974) * q^93 + (2142047924273965502890717777b2 - 963223082433629552240227451b1 - 1285800823754378682776184271) * q^94 + (3599389253933772504778249166b2 + 13987183819235700886876216769b1 + 18819848371227828667132594673) * q^96 + (-1391919259584383121915799826b2 - 5408981683229597201126202959b1) * q^98
$\operatorname{Tr}(f)(q)$	$=$	$3 q + 805306368 q^{4} + 406329814947 q^{6} - 26346547412877 q^{8} + 68630377364883 q^{9} - 64\!\cdots\!41 q^{12} + 21\!\cdots\!08 q^{16} - 99\!\cdots\!77 q^{18} + 34\!\cdots\!27 q^{23} + 10\!\cdots\!32 q^{24}+ \cdots + 56\!\cdots\!19 q^{96}+O(q^{100})$ 3 * q + 805306368 * q^4 + 406329814947 * q^6 - 26346547412877 * q^8 + 68630377364883 * q^9 - 6428874064093341 * q^12 + 216172782113783808 * q^16 - 998464372720674477 * q^18 + 34778508973616249427 * q^23 + 109073329161693560832 * q^24 + 111758708953857421875 * q^25 + 160812091478972670387 * q^26 + 44095279340037350838 * q^27 - 7072347468801257766912 * q^32 + 36611812861559975045955 * q^36 + 92285315998575040627302 * q^39 - 3568462578255557671624173 * q^48 + 1379959609634219882930403 * q^49 - 2306297153127655570412397 * q^52 + 9295522844805228962102067 * q^54 - 29199066724751619211125501 * q^58 + 37142086974723088377739062 * q^59 - 53927575691102536570638141 * q^62 + 173351747518156380249242595 * q^64 - 870747736260205021954989309 * q^72 + 285879692636347860605531523 * q^78 + 1570042899082081611640534563 * q^81 + 3133958059624367453189786403 * q^82 - 7110096945944459493910428762 * q^87 + 9335784915332769883946483712 * q^92 - 21136154306325351781700018922 * q^93 - 3857402471263136048328552813 * q^94 + 56459545113683486001397784019 * q^96

$\beta_{1}$	$=$	$\nu$ v
$\beta_{2}$	$=$	$\nu^{2} - \nu - 4$ v^2 - v - 4

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