LMFDB - Newform orbit 23.23.b.a

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [23,23,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, 23, names="a")

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

chi := DirichletCharacter("23.22");

S:= CuspForms(chi, 23);

N := Newforms(S);

Level:	$N$	$=$	$23$
Weight:	$k$	$=$	$23$
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:	$70.5427100136$
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:	$\Z[a_1, a_2, a_3]$
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

−2.14510
2.66908
−0.523976

−4079.59

−97708.1

1.24488e7

3.98609e8

−3.36749e10

−2.18342e10

22.2

1722.63

343783.

−1.22684e6

5.92212e8

−9.33864e9

8.68056e10

22.3

2356.96

−246075.

1.36096e6

−5.79989e8

−6.67807e9

2.91718e10

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	23.23.b.a	✓	3
23.b	odd	2	1	CM	23.23.b.a	✓	3

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

This newform subspace can be constructed as the kernel of the linear operator $T_{2}^{3} - 12582912T_{2} + 16563886423$ T2^3 - 12582912*T2 + 16563886423 acting on $S_{23}^{\mathrm{new}}(23, [\chi])$ .

Hecke characteristic polynomials

$p$	$F_p(T)$
$2$	$T^{3} + \cdots + 16563886423$ T^3 - 12582912*T + 16563886423
$3$	$T^{3} + \cdots - 82\!\cdots\!58$ T^3 - 94143178827*T - 8265743463387658
$5$	$T^{3}$ T^3
$7$	$T^{3}$ T^3
$11$	$T^{3}$ T^3
$13$	$T^{3} + \cdots + 45\!\cdots\!62$ T^3 - 9635516633864565315472107*T + 4533397208496029210418120650397954262
$17$	$T^{3}$ T^3
$19$	$T^{3}$ T^3
$23$	$(T + 952809757913927)^{3}$ (T + 952809757913927)^3
$29$	$T^{3} + \cdots + 34\!\cdots\!74$ T^3 - 446557315629249907318015693731723*T + 3409082718405996255768945091343397243511765841974
$31$	$T^{3} + \cdots + 85\!\cdots\!86$ T^3 - 1936772094585414219110199120415683*T + 8598473799466180618227345059019105456606702885886
$37$	$T^{3}$ T^3
$41$	$T^{3} + \cdots - 13\!\cdots\!74$ T^3 - 908586129449230747483779513704791443*T - 130244325175043389539550027701237643416077159809557074
$43$	$T^{3}$ T^3
$47$	$T^{3} + \cdots - 20\!\cdots\!62$ T^3 - 18334713554174399409230107071166091427*T - 2094696967136054456409674840173136617322226225562956962
$53$	$T^{3}$ T^3
$59$	$(T + 38\!\cdots\!94)^{3}$ (T + 38752837757877706294)^3
$61$	$T^{3}$ T^3
$67$	$T^{3}$ T^3
$71$	$T^{3} + \cdots + 14\!\cdots\!26$ T^3 - 160252541746767460276960539760234419910323*T + 14602502665689723659134042124363408986762174532091533040168526
$73$	$T^{3} + \cdots + 36\!\cdots\!42$ T^3 - 295273299713125319149195915789165451922387*T + 36338832693768818950595733392205466586775528883364455667551342
$79$	$T^{3}$ 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 $\F_{q}$

$f(q)$	$=$	$q + ( - 866 \beta_{2} + 793 \beta_1) q^{2} + (57383 \beta_{2} + 119022 \beta_1) q^{3} + (1252369 \beta_{2} - 2244539 \beta_1 + 4194304) q^{4} + (201646457 \beta_{2} + \cdots + 136944049) q^{6} + ( - 3632267264 \beta_{2} + \cdots - 16563886423) q^{8}+ \cdots + ( - 33\!\cdots\!34 \beta_{2} + 31\!\cdots\!57 \beta_1) q^{98}+O(q^{100})$ q + (-866b2 + 793b1) * q^2 + (57383b2 + 119022b1) * q^3 + (1252369b2 - 2244539b1 + 4194304) * q^4 + (201646457b2 + 136203469b1 + 136944049) * q^6 + (-3632267264b2 + 3326083072b1 - 16563886423) * q^8 + (-2786251057b2 + 21240297958b1 + 31381059609) * q^9 + (-118593546434b2 + 108596630857b1 - 657671023151) * q^12 + (886984458031b2 + 910933052206b1) * q^13 + (14344325642318b2 - 13135161933439b1 + 17592186044416) * q^16 + (7858260363767b2 + 16299354600078b1 + 102455180734777) * q^18 - 952809757913927 * q^23 + (-104718953430081b2 - 1400188134997730b1 + 574384972496896) * q^24 + 2384185791015625 * q^25 + (1575987799046017b2 + 2173137643717237b1 - 1633802254339831) * q^26 + (1800739343543247b2 + 3735036476782398b1 + 8265743463387658) * q^27 + (6866049457758103b2 + 4296954426227566b1) * q^29 + (-4065217780535513b2 + 16276446360275734b1) * q^31 + (-20744097875686087b2 + 37178289067993997b1 - 69473975079534592) * q^32 + (-49425520274853161b2 + 10810946168952910b1 - 112868031285752735) * q^36 + (-100319490914032921b2 + 164468150927779366b1 + 581228534391304786) * q^39 + (-272174748836229449b2 - 280039734549046586b1) * q^41 + (825133250353460782b2 - 755578138025744111b1) * q^46 + (-1386647499567539441b2 + 193498393714195414b1) * q^47 + (-2330556599561629983b2 - 162201623556120235b1 - 2268325673941746727) * q^48 + 3909821048582988049 * q^49 + (-2064704895019531250b2 + 1890659332275390625b1) * q^50 + (1414872752258293646b2 - 1295605187691485983b1 - 663461123156392807) * q^52 + (-830254352233056515b2 + 10828943746107996415b1 + 4297449364766816841) * q^54 + (7629869003527873513b2 + 17023097207724597757b1 - 23769668229406367359) * q^58 - 38752837757877706294 * q^59 + (26705863613718350257b2 - 11452855480152298907b1 + 90070879690420601249) * q^62 + (60164462418876956672b2 - 55092862238070931456b1 + 200575357139205528465) * q^64 + (-54675082338374873041b2 - 113405323006431419394b1) * q^69 + (-82485715378314450353b2 - 150729693083166255098b1) * q^71 + (79111078930901082279b2 - 283457434770465268522b1 - 90064132820270678399) * q^72 + (-71375450506343083769b2 + 186824008935649266502b1) * q^73 + (136811733245849609375b2 + 283770561218261718750b1) * q^75 + (-237814571230408379715b2 + 195601338196643676055b1 + 1264935824530516243777) * q^78 + (474313157159573979014b2 + 983805318499325830476b1 + 984770902183611232881) * q^81 + (-484454676281913035951b2 - 666798340189398957947b1 + 499254122671128055793) * q^82 + (-946345480717577219041b2 + 787226152050892266598b1 + 3345912460679527433458) * q^87 + (-1193269403708906843063b2 + 2138618661218367794653b1 - 3996373778857415671808) * q^92 + (1720388619776403138791b2 + 2853944953310481712942b1 + 5899233472551332977882) * q^93 + (219788567703419812633b2 - 3515410319149173353747b1 + 9085978388727914793881) * q^94 + (1964370033633552665582b2 - 1798782259435805154511b1 + 10893588131171367578873) * q^96 + (-3385905028072867650434b2 + 3100488091526309522857b1) * q^98
$\operatorname{Tr}(f)(q)$	$=$	$3 q + 12582912 q^{4} + 410832147 q^{6} - 49691659269 q^{8} + 94143178827 q^{9} - 1973013069453 q^{12} + 52776558133248 q^{16} + 307365542204331 q^{18} - 28\!\cdots\!81 q^{23} + 17\!\cdots\!88 q^{24} + 71\!\cdots\!75 q^{25}+ \cdots + 32\!\cdots\!19 q^{96}+O(q^{100})$ 3 * q + 12582912 * q^4 + 410832147 * q^6 - 49691659269 * q^8 + 94143178827 * q^9 - 1973013069453 * q^12 + 52776558133248 * q^16 + 307365542204331 * q^18 - 2858429273741781 * q^23 + 1723154917490688 * q^24 + 7152557373046875 * q^25 - 4901406763019493 * q^26 + 24797230390162974 * q^27 - 208421925238603776 * q^32 - 338604093857258205 * q^36 + 1743685603173914358 * q^39 - 6804977021825240181 * q^48 + 11729463145748964147 * q^49 - 1990383369469178421 * q^52 + 12892348094300450523 * q^54 - 71309004688219102077 * q^58 - 116258513273633118882 * q^59 + 270212639071261803747 * q^62 + 601726071417616585395 * q^64 - 270192398460812035197 * q^72 + 3794807473591548731331 * q^78 + 2954312706550833698643 * q^81 + 1497762368013384167379 * q^82 + 10037737382038582300374 * q^87 - 11989121336572247015424 * q^92 + 17697700417653998933646 * q^93 + 27257935166183744381643 * q^94 + 32680764393514102736619 * q^96

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

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