LMFDB - Newform orbit 633.2.j.a

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [633,2,Mod(58,633)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(633, base_ring=CyclotomicField(14))

chi = DirichletCharacter(H, H._module([0, 12]))

N = Newforms(chi, 2, names="a")

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

chi := DirichletCharacter("633.58");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 633 = 3 \cdot 211 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	633.j (of order $7$, degree $6$, 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:	no
Analytic conductor:	$5.05453044795$
Analytic rank:	$0$
Dimension:	$102$
Relative dimension:	$17$ over $\Q(\zeta_{7})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{7}]$

$q$-expansion

The dimension is sufficiently large that we do not compute an algebraic $q$-expansion, but we have computed the trace expansion.

$\operatorname{Tr}(f)(q) = $ $ 102 q + 7 q^{2} + 17 q^{3} - 23 q^{4} + 2 q^{5} + 7 q^{6} + 2 q^{7} + q^{8} - 17 q^{9}+O(q^{10}) $

$\operatorname{Tr}(f)(q) = $ \( 102 q + 7 q^{2} + 17 q^{3} - 23 q^{4} + 2 q^{5} + 7 q^{6} + 2 q^{7} + q^{8} - 17 q^{9} + 12 q^{10} - 6 q^{11} + 9 q^{12} + 6 q^{13} - 10 q^{14} + 12 q^{15} + 21 q^{16} + 3 q^{17} + 16 q^{19} + 10 q^{20} + 12 q^{21} + 12 q^{22} + 30 q^{23} - q^{24} + 9 q^{25} - 29 q^{26} + 17 q^{27} - 30 q^{28} + 9 q^{29} - 33 q^{30} + 34 q^{31} - 13 q^{32} - 8 q^{33} - 47 q^{34} - 29 q^{35} - 9 q^{36} + 17 q^{37} - 23 q^{38} + q^{39} - 26 q^{40} + 12 q^{41} - 11 q^{42} - 11 q^{43} + 37 q^{44} + 2 q^{45} + 27 q^{46} - 12 q^{47} + 28 q^{48} - 37 q^{49} + 98 q^{50} - 3 q^{51} - 4 q^{52} - q^{53} + 26 q^{55} - 81 q^{56} - 2 q^{57} + 15 q^{58} - 39 q^{59} - 10 q^{60} + 116 q^{61} + 61 q^{62} + 2 q^{63} + 33 q^{64} + 45 q^{65} + 9 q^{66} - 85 q^{67} - 83 q^{68} - 2 q^{69} - 8 q^{70} + 36 q^{71} - 20 q^{72} - 25 q^{73} - 76 q^{74} + 5 q^{75} + 56 q^{76} + 76 q^{77} - 6 q^{78} - 14 q^{79} - 124 q^{80} - 17 q^{81} + 23 q^{82} + 14 q^{83} - 19 q^{84} + 67 q^{85} + 61 q^{86} + 12 q^{87} - 123 q^{88} - 20 q^{89} - 23 q^{90} - 54 q^{91} + q^{92} - 34 q^{93} + 65 q^{94} + 19 q^{95} - 64 q^{96} - 30 q^{97} - 57 q^{98} + 8 q^{99}+O(q^{100}) \)

102 * q + 7 * q^2 + 17 * q^3 - 23 * q^4 + 2 * q^5 + 7 * q^6 + 2 * q^7 + q^8 - 17 * q^9 + 12 * q^10 - 6 * q^11 + 9 * q^12 + 6 * q^13 - 10 * q^14 + 12 * q^15 + 21 * q^16 + 3 * q^17 + 16 * q^19 + 10 * q^20 + 12 * q^21 + 12 * q^22 + 30 * q^23 - q^24 + 9 * q^25 - 29 * q^26 + 17 * q^27 - 30 * q^28 + 9 * q^29 - 33 * q^30 + 34 * q^31 - 13 * q^32 - 8 * q^33 - 47 * q^34 - 29 * q^35 - 9 * q^36 + 17 * q^37 - 23 * q^38 + q^39 - 26 * q^40 + 12 * q^41 - 11 * q^42 - 11 * q^43 + 37 * q^44 + 2 * q^45 + 27 * q^46 - 12 * q^47 + 28 * q^48 - 37 * q^49 + 98 * q^50 - 3 * q^51 - 4 * q^52 - q^53 + 26 * q^55 - 81 * q^56 - 2 * q^57 + 15 * q^58 - 39 * q^59 - 10 * q^60 + 116 * q^61 + 61 * q^62 + 2 * q^63 + 33 * q^64 + 45 * q^65 + 9 * q^66 - 85 * q^67 - 83 * q^68 - 2 * q^69 - 8 * q^70 + 36 * q^71 - 20 * q^72 - 25 * q^73 - 76 * q^74 + 5 * q^75 + 56 * q^76 + 76 * q^77 - 6 * q^78 - 14 * q^79 - 124 * q^80 - 17 * q^81 + 23 * q^82 + 14 * q^83 - 19 * q^84 + 67 * q^85 + 61 * q^86 + 12 * q^87 - 123 * q^88 - 20 * q^89 - 23 * q^90 - 54 * q^91 + q^92 - 34 * q^93 + 65 * q^94 + 19 * q^95 - 64 * q^96 - 30 * q^97 - 57 * q^98 + 8 * q^99

Display 100 coefficients 10 coefficients

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	$ a_{2} $			$ a_{3} $			$ a_{4} $			$ a_{5} $			$ a_{6} $			$ a_{7} $			$ a_{8} $			$ a_{9} $			$ a_{10} $
58.1	−2.21227	+	1.06537i	0.900969	−	0.433884i	2.51213	−	3.15011i	−1.86917	−	0.900145i	−1.53094	+	1.91973i	1.35248	+	0.651320i	−1.10869	+	4.85750i	0.623490	−	0.781831i	5.09409
58.2	−1.93212	+	0.930459i	0.900969	−	0.433884i	1.62035	−	2.03185i	2.34489	+	1.12924i	−1.33707	+	1.67663i	3.74099	+	1.80157i	−0.285760	+	1.25199i	0.623490	−	0.781831i	−5.58131
58.3	−1.58514	+	0.763365i	0.900969	−	0.433884i	0.682973	−	0.856421i	0.879581	+	0.423584i	−1.09695	+	1.37554i	−0.768799	−	0.370234i	0.354148	−	1.55162i	0.623490	−	0.781831i	−1.71761
58.4	−1.57317	+	0.757599i	0.900969	−	0.433884i	0.653928	−	0.820000i	2.94852	+	1.41993i	−1.08867	+	1.36515i	−3.44433	−	1.65870i	0.369573	−	1.61920i	0.623490	−	0.781831i	−5.71427
58.5	−1.20842	+	0.581942i	0.900969	−	0.433884i	−0.125368	+	0.157206i	−1.83291	−	0.882682i	−0.836250	+	1.04862i	2.67459	+	1.28801i	0.656920	−	2.87815i	0.623490	−	0.781831i	2.72858
58.6	−0.943455	+	0.454344i	0.900969	−	0.433884i	−0.563301	+	0.706357i	−0.330692	−	0.159253i	−0.652891	+	0.818699i	−1.89870	−	0.914364i	0.676548	−	2.96415i	0.623490	−	0.781831i	0.384348
58.7	−0.505165	+	0.243275i	0.900969	−	0.433884i	−1.05097	+	1.31788i	1.33325	+	0.642061i	−0.349585	+	0.438366i	4.43429	+	2.13544i	0.459839	−	2.01468i	0.623490	−	0.781831i	−0.829709
58.8	−0.164045	+	0.0789998i	0.900969	−	0.433884i	−1.22631	+	1.53774i	−0.727443	−	0.350318i	−0.113522	+	0.142353i	−2.28528	−	1.10053i	0.160720	−	0.704159i	0.623490	−	0.781831i	0.147008
58.9	0.212087	−	0.102136i	0.900969	−	0.433884i	−1.21243	+	1.52034i	3.49335	+	1.68231i	0.146769	−	0.184042i	−0.300233	−	0.144584i	−0.206622	+	0.905271i	0.623490	−	0.781831i	0.912719
58.10	0.598572	−	0.288257i	0.900969	−	0.433884i	−0.971783	+	1.21858i	−3.20197	−	1.54199i	0.414225	−	0.519421i	0.853343	+	0.410948i	−0.526089	+	2.30495i	0.623490	−	0.781831i	−2.36110
58.11	0.976127	−	0.470078i	0.900969	−	0.433884i	−0.515129	+	0.645952i	−2.03757	−	0.981242i	0.675501	−	0.847051i	−3.01329	−	1.45113i	−0.681351	+	2.98519i	0.623490	−	0.781831i	−2.45019
58.12	1.11057	−	0.534825i	0.900969	−	0.433884i	−0.299641	+	0.375738i	1.61591	+	0.778181i	0.768542	−	0.963721i	2.46010	+	1.18472i	−0.680398	+	2.98102i	0.623490	−	0.781831i	2.21078
58.13	1.45965	−	0.702932i	0.900969	−	0.433884i	0.389494	−	0.488410i	−1.34325	−	0.646875i	1.01011	−	1.26664i	2.08862	+	1.00583i	−0.495802	+	2.17225i	0.623490	−	0.781831i	−2.41539
58.14	1.86290	−	0.897123i	0.900969	−	0.433884i	1.41857	−	1.77883i	3.29234	+	1.58551i	1.28916	−	1.61656i	−2.98252	−	1.43631i	0.126624	−	0.554777i	0.623490	−	0.781831i	7.55568
58.15	2.07373	−	0.998654i	0.900969	−	0.433884i	2.05605	−	2.57821i	0.490877	+	0.236394i	1.43506	−	1.79951i	1.33815	+	0.644421i	0.664617	−	2.91188i	0.623490	−	0.781831i	1.25402
58.16	2.26941	−	1.09289i	0.900969	−	0.433884i	2.70882	−	3.39676i	−3.64441	−	1.75506i	1.57048	−	1.96932i	−1.39201	−	0.670354i	1.31415	−	5.75766i	0.623490	−	0.781831i	−10.1887
58.17	2.30771	−	1.11134i	0.900969	−	0.433884i	2.84349	−	3.56563i	0.390632	+	0.188118i	1.59699	−	2.00256i	−1.05547	−	0.508287i	1.45944	−	6.39423i	0.623490	−	0.781831i	1.11053
148.1	−0.602159	+	2.63823i	0.222521	−	0.974928i	−4.79572	−	2.30950i	0.309249	+	1.35491i	2.43809	+	1.17412i	−0.0645022	−	0.282603i	5.60635	−	7.03014i	−0.900969	−	0.433884i	−3.76077
148.2	−0.541227	+	2.37127i	0.222521	−	0.974928i	−3.52806	−	1.69902i	−0.152066	−	0.666245i	2.19138	+	1.05531i	−0.974227	−	4.26837i	2.90536	−	3.64321i	−0.900969	−	0.433884i	1.66215
148.3	−0.488725	+	2.14124i	0.222521	−	0.974928i	−2.54414	−	1.22519i	−0.496014	−	2.17318i	1.97881	+	0.952944i	0.265170	+	1.16178i	1.12807	−	1.41455i	−0.900969	−	0.433884i	4.89572

See next 80 embeddings (of 102 total)

Inner twists

Char	Parity	Ord	Mult	Type
1.a	even	1	1	trivial
211.f	even	7	1	inner

Twists

By twisting character orbit
Char	Parity	Ord	Mult	Type	Twist	Min	Dim
1.a	even	1	1	trivial	633.2.j.a	✓	102
211.f	even	7	1	inner	633.2.j.a	✓	102

By twisted newform orbit
Twist	Min	Dim	Char	Parity	Ord	Mult	Type
633.2.j.a	✓	102	1.a	even	1	1	trivial
633.2.j.a	✓	102	211.f	even	7	1	inner

Hecke kernels

This newform subspace can be constructed as the kernel of the linear operator $ T_{2}^{102} - 7 T_{2}^{101} + 53 T_{2}^{100} - 257 T_{2}^{99} + 1249 T_{2}^{98} - 4863 T_{2}^{97} + \cdots + 482197681 $ T2^102 - 7*T2^101 + 53*T2^100 - 257*T2^99 + 1249*T2^98 - 4863*T2^97 + 18925*T2^96 - 63824*T2^95 + 217082*T2^94 - 663897*T2^93 + 2067721*T2^92 - 5896139*T2^91 + 17293602*T2^90 - 46931274*T2^89 + 131708180*T2^88 - 343623950*T2^87 + 928124491*T2^86 - 2330190586*T2^85 + 6056724827*T2^84 - 14606476639*T2^83 + 36544155390*T2^82 - 84666032665*T2^81 + 204419947327*T2^80 - 455945570355*T2^79 + 1066556510545*T2^78 - 2298803595183*T2^77 + 5229688833967*T2^76 - 10911853658769*T2^75 + 24179595570458*T2^74 - 48784763273677*T2^73 + 105188264350043*T2^72 - 204745708647067*T2^71 + 429384638604144*T2^70 - 805620132554091*T2^69 + 1645097096779989*T2^68 - 2978439567945246*T2^67 + 5936862112012608*T2^66 - 10397904764285537*T2^65 + 20286416166122530*T2^64 - 34388064338940647*T2^63 + 65658705768543811*T2^62 - 107510692680590623*T2^61 + 200253270976680516*T2^60 - 316246469800134508*T2^59 + 573676632080584125*T2^58 - 875876249373616348*T2^57 + 1545920049709100345*T2^56 - 2290015173602238521*T2^55 + 3926524661582867063*T2^54 - 5645764663153353137*T2^53 + 9398982031444981935*T2^52 - 13054027064350077142*T2^51 + 21022533466550499956*T2^50 - 28110772628609054582*T2^49 + 43402694975169596215*T2^48 - 55856380522480486148*T2^47 + 82517366051389637452*T2^46 - 102510032818574404183*T2^45 + 145525948359738142097*T2^44 - 175104553886356494088*T2^43 + 239333794190881065947*T2^42 - 279975637262244165423*T2^41 + 368648096910943111034*T2^40 - 415141913840165808420*T2^39 + 522160781534349479639*T2^38 - 560353100174201394846*T2^37 + 657410359551144621688*T2^36 - 658964073037829329528*T2^35 + 736104445563502307155*T2^34 - 707969136275977712601*T2^33 + 753211599960641934425*T2^32 - 692066975537509672856*T2^31 + 718467797480660747218*T2^30 - 640614969347591520804*T2^29 + 637837774371781091677*T2^28 - 542173778932548516186*T2^27 + 501038500433722127905*T2^26 - 372615579376156207928*T2^25 + 285916423223675186645*T2^24 - 172528382820503196857*T2^23 + 115511029463594821600*T2^22 - 63687300771350695041*T2^21 + 40649399829211107342*T2^20 - 18488446882180182347*T2^19 + 10040426391102002537*T2^18 - 4081569093826702906*T2^17 + 3336764108650674998*T2^16 - 1816587214547521066*T2^15 + 1240630854127051718*T2^14 - 393205818276100424*T2^13 + 179105631183929227*T2^12 - 40205264466670527*T2^11 + 19780533172974168*T2^10 - 3487539745441367*T2^9 + 1309984727844569*T2^8 - 101489235319283*T2^7 + 16740592101744*T2^6 - 2125997599390*T2^5 - 120478341046*T2^4 + 222920774832*T2^3 + 123091448277*T2^2 - 2693205473*T2 + 482197681 acting on $S_{2}^{\mathrm{new}}(633, [\chi])$.

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 633 = 3 \cdot 211 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	633.j (of order \(7\), degree \(6\), minimal)

\(n\):		e.g. 2-40 or 990-1000
Embeddings:		e.g. 1-3 or 58.17
Significant digits:
Format:

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