LMFDB - Newform orbit 930.2.bj.b

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [930,2,Mod(277,930)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(930, base_ring=CyclotomicField(20))

chi = DirichletCharacter(H, H._module([0, 5, 6]))

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

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

chi := DirichletCharacter("930.277");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 930 = 2 \cdot 3 \cdot 5 \cdot 31 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	930.bj (of order $20$, degree $8$, 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:	$7.42608738798$
Analytic rank:	$0$
Dimension:	$128$
Relative dimension:	$16$ over $\Q(\zeta_{20})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{20}]$

$q$-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) = $ $ 128 q + 4 q^{7}+O(q^{10}) $

$\operatorname{Tr}(f)(q) = $ $ 128 q + 4 q^{7} - 4 q^{10} - 4 q^{15} + 32 q^{16} + 12 q^{17} + 40 q^{19} + 40 q^{21} + 4 q^{22} + 32 q^{24} - 8 q^{25} - 4 q^{28} - 8 q^{29} + 20 q^{31} + 4 q^{33} + 24 q^{35} - 128 q^{36} - 64 q^{37} - 16 q^{38} - 24 q^{41} + 16 q^{42} - 24 q^{43} + 8 q^{44} + 20 q^{46} - 12 q^{47} + 100 q^{49} - 24 q^{50} + 64 q^{53} + 32 q^{54} + 68 q^{55} - 16 q^{57} + 40 q^{58} + 8 q^{62} - 4 q^{63} + 84 q^{65} - 12 q^{66} - 32 q^{67} - 8 q^{68} + 88 q^{70} + 24 q^{71} + 20 q^{73} + 16 q^{74} - 24 q^{75} - 24 q^{76} + 60 q^{77} + 56 q^{79} + 32 q^{81} - 16 q^{82} + 8 q^{83} - 68 q^{85} - 20 q^{87} + 4 q^{88} - 136 q^{89} - 40 q^{91} + 48 q^{93} - 92 q^{95} + 64 q^{97} - 16 q^{98} + 8 q^{99}+O(q^{100}) $

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_{7} $			$ a_{8} $			$ a_{9} $			$ a_{10} $
277.1	−0.156434	−	0.987688i	−0.987688	−	0.156434i	−0.951057	+	0.309017i	−1.90277	+	1.17451i	1.00000i	1.72531	−	3.38612i	0.453990	+	0.891007i	0.951057	+	0.309017i	1.45771	+	1.69561i
277.2	−0.156434	−	0.987688i	−0.987688	−	0.156434i	−0.951057	+	0.309017i	−1.82843	+	1.28719i	1.00000i	−2.04975	+	4.02286i	0.453990	+	0.891007i	0.951057	+	0.309017i	1.55737	+	1.60455i
277.3	−0.156434	−	0.987688i	−0.987688	−	0.156434i	−0.951057	+	0.309017i	−1.74178	−	1.40221i	1.00000i	−0.335285	+	0.658034i	0.453990	+	0.891007i	0.951057	+	0.309017i	−1.11247	+	1.93969i
277.4	−0.156434	−	0.987688i	−0.987688	−	0.156434i	−0.951057	+	0.309017i	−1.67223	−	1.48447i	1.00000i	1.10706	−	2.17272i	0.453990	+	0.891007i	0.951057	+	0.309017i	−1.20460	+	1.88386i
277.5	−0.156434	−	0.987688i	−0.987688	−	0.156434i	−0.951057	+	0.309017i	0.244623	+	2.22265i	1.00000i	0.795365	−	1.56099i	0.453990	+	0.891007i	0.951057	+	0.309017i	2.15702	−	0.589310i
277.6	−0.156434	−	0.987688i	−0.987688	−	0.156434i	−0.951057	+	0.309017i	1.48798	−	1.66911i	1.00000i	−0.506200	+	0.993473i	0.453990	+	0.891007i	0.951057	+	0.309017i	−1.88133	−	1.20856i
277.7	−0.156434	−	0.987688i	−0.987688	−	0.156434i	−0.951057	+	0.309017i	1.61098	−	1.55073i	1.00000i	−1.36477	+	2.67852i	0.453990	+	0.891007i	0.951057	+	0.309017i	−1.78365	−	1.34855i
277.8	−0.156434	−	0.987688i	−0.987688	−	0.156434i	−0.951057	+	0.309017i	2.17207	+	0.531157i	1.00000i	0.369895	−	0.725959i	0.453990	+	0.891007i	0.951057	+	0.309017i	0.184831	−	2.22842i
277.9	0.156434	+	0.987688i	0.987688	+	0.156434i	−0.951057	+	0.309017i	−2.23524	−	0.0607951i	1.00000i	0.773249	−	1.51759i	−0.453990	−	0.891007i	0.951057	+	0.309017i	−0.289622	−	2.21723i
277.10	0.156434	+	0.987688i	0.987688	+	0.156434i	−0.951057	+	0.309017i	−2.20784	+	0.354206i	1.00000i	0.622042	−	1.22083i	−0.453990	−	0.891007i	0.951057	+	0.309017i	−0.695226	−	2.12524i
277.11	0.156434	+	0.987688i	0.987688	+	0.156434i	−0.951057	+	0.309017i	−1.01777	−	1.99102i	1.00000i	−0.681739	+	1.33799i	−0.453990	−	0.891007i	0.951057	+	0.309017i	1.80729	−	1.31670i
277.12	0.156434	+	0.987688i	0.987688	+	0.156434i	−0.951057	+	0.309017i	−0.869928	+	2.05991i	1.00000i	−2.25496	+	4.42561i	−0.453990	−	0.891007i	0.951057	+	0.309017i	−2.17063	−	0.536977i
277.13	0.156434	+	0.987688i	0.987688	+	0.156434i	−0.951057	+	0.309017i	0.145083	+	2.23136i	1.00000i	0.996252	−	1.95526i	−0.453990	−	0.891007i	0.951057	+	0.309017i	−2.18119	+	0.492358i
277.14	0.156434	+	0.987688i	0.987688	+	0.156434i	−0.951057	+	0.309017i	1.00799	−	1.99598i	1.00000i	1.85184	−	3.63444i	−0.453990	−	0.891007i	0.951057	+	0.309017i	2.12909	+	0.683342i
277.15	0.156434	+	0.987688i	0.987688	+	0.156434i	−0.951057	+	0.309017i	2.22022	+	0.265769i	1.00000i	1.65375	−	3.24566i	−0.453990	−	0.891007i	0.951057	+	0.309017i	0.0848219	+	2.23446i
277.16	0.156434	+	0.987688i	0.987688	+	0.156434i	−0.951057	+	0.309017i	2.23590	+	0.0275636i	1.00000i	−1.08401	+	2.12750i	−0.453990	−	0.891007i	0.951057	+	0.309017i	0.322547	+	2.21268i
337.1	−0.453990	+	0.891007i	0.891007	−	0.453990i	−0.587785	−	0.809017i	−2.20246	+	0.386226i	1.00000i	3.54459	+	0.561408i	0.987688	−	0.156434i	0.587785	−	0.809017i	0.655766	−	2.13775i
337.2	−0.453990	+	0.891007i	0.891007	−	0.453990i	−0.587785	−	0.809017i	−1.81236	−	1.30972i	1.00000i	−2.09145	−	0.331253i	0.987688	−	0.156434i	0.587785	−	0.809017i	1.98976	−	1.02022i
337.3	−0.453990	+	0.891007i	0.891007	−	0.453990i	−0.587785	−	0.809017i	−1.39059	+	1.75108i	1.00000i	−2.23420	−	0.353863i	0.987688	−	0.156434i	0.587785	−	0.809017i	−0.928908	−	2.03399i
337.4	−0.453990	+	0.891007i	0.891007	−	0.453990i	−0.587785	−	0.809017i	−0.354402	−	2.20780i	1.00000i	5.01200	+	0.793822i	0.987688	−	0.156434i	0.587785	−	0.809017i	2.12806	+	0.686548i

See next 80 embeddings (of 128 total)

Inner twists

Char	Parity	Ord	Mult	Type
1.a	even	1	1	trivial
155.r	even	20	1	inner

Twists

By twisting character orbit
Char	Parity	Ord	Mult	Type	Twist	Min	Dim
1.a	even	1	1	trivial	930.2.bj.b	yes	128
5.c	odd	4	1		930.2.bj.a	✓	128
31.f	odd	10	1		930.2.bj.a	✓	128
155.r	even	20	1	inner	930.2.bj.b	yes	128

By twisted newform orbit
Twist	Min	Dim	Char	Parity	Ord	Mult	Type
930.2.bj.a	✓	128	5.c	odd	4	1
930.2.bj.a	✓	128	31.f	odd	10	1
930.2.bj.b	yes	128	1.a	even	1	1	trivial
930.2.bj.b	yes	128	155.r	even	20	1	inner

Hecke kernels

This newform subspace can be constructed as the kernel of the linear operator $ T_{7}^{128} - 4 T_{7}^{127} - 42 T_{7}^{126} + 84 T_{7}^{125} + 475 T_{7}^{124} + 3256 T_{7}^{123} + \cdots + 34\!\cdots\!76 $ T7^128 - 4*T7^127 - 42*T7^126 + 84*T7^125 + 475*T7^124 + 3256*T7^123 + 4044*T7^122 - 127580*T7^121 + 108383*T7^120 - 269932*T7^119 - 5811848*T7^118 + 58780240*T7^117 - 118646475*T7^116 + 254676752*T7^115 + 4947591508*T7^114 - 38265251568*T7^113 + 49506777602*T7^112 + 102498439348*T7^111 - 2310602585592*T7^110 + 13725905798936*T7^109 - 14789737146271*T7^108 - 70248223113672*T7^107 + 902969070274612*T7^106 - 5112767721240388*T7^105 + 7321834028047975*T7^104 + 39126505183015044*T7^103 - 376248364661645818*T7^102 + 1496046067511002280*T7^101 - 1040590324216858908*T7^100 - 15759288532419552560*T7^99 + 110277998832776165380*T7^98 - 333090086983111300424*T7^97 - 331809051077718839757*T7^96 + 5792587167710654716792*T7^95 - 20147580484703836454488*T7^94 + 19284453138997154245756*T7^93 + 169136529447864225537852*T7^92 - 921879365285701377829096*T7^91 + 2008233603213732639280936*T7^90 + 1954224004660013729713580*T7^89 - 32175573468089248268701423*T7^88 + 91252382950391889608112908*T7^87 - 19066794201364098642970710*T7^86 - 547711529639733520308760368*T7^85 + 2137966940761823093305710123*T7^84 - 4705794484793035237723480116*T7^83 + 2840003824010375664414372440*T7^82 + 30040826484995398130517270320*T7^81 - 194131461743718549108101482431*T7^80 + 536690176791997949151342062264*T7^79 + 16353813861577069803295318336*T7^78 - 5077839178667553388574980405912*T7^77 + 17072789672482614572091252479605*T7^76 - 14858752631610480472032850784408*T7^75 - 80290687866636994262555591620132*T7^74 + 332510761196642482881683725981848*T7^73 - 488299803658711200701677870995526*T7^72 - 431789244235314438205011597265104*T7^71 + 4029669202784119193413032650031688*T7^70 - 10086431782124748558006781972413432*T7^69 + 11282757262740567293608384653501879*T7^68 + 17199731623334073041377614205323288*T7^67 - 132857971034645495004287219224557788*T7^66 + 361587892289216309414323891748062136*T7^65 - 400793805822858885299883956499933659*T7^64 - 890892531717156906549848018053148912*T7^63 + 5234515814769186227014404565423876578*T7^62 - 10781574300731861373113408756678140936*T7^61 + 3605703291547737326093193758238523336*T7^60 + 43646499794052154511550895471221169260*T7^59 - 138572183376555055608179337792916659700*T7^58 + 172587720533897479075758838089630734272*T7^57 + 153202509334221785930826405867648793301*T7^56 - 1106693198506958038305412525810841439956*T7^55 + 2193046912840219360574411659952468070944*T7^54 - 1191495162822596687072075715769063229336*T7^53 - 5139568071901277874087928656547959413492*T7^52 + 16229690664981813821873056244313220358844*T7^51 - 20920178229035975775349469767100823818656*T7^50 - 3181852058887457492473807201404503147112*T7^49 + 70875899014705146956894184315386148124459*T7^48 - 149820918120557300372895082489334843621604*T7^47 + 137601517044409619541441838478575305039246*T7^46 + 103530888770682618939752330906945273919544*T7^45 - 599991482192520602182656842274753784111107*T7^44 + 1043888892262495604545762963532378033605388*T7^43 - 797204609570204207400597860592439383556896*T7^42 - 793565028351362802772884669176306645844196*T7^41 + 3724085649570543536889459091743737303652311*T7^40 - 6348722537656104310739905547761542873799448*T7^39 + 5278483298370401862283764042422682221221176*T7^38 + 3656752034457635702185681259435957737856920*T7^37 - 20520206535771754627839213013012365492530933*T7^36 + 35127693939137938568113253456347298702137668*T7^35 - 28873824873148526378751314958386011834463180*T7^34 - 11979542217285238560577205968664847581181812*T7^33 + 82954395661449132664397209270157314308942554*T7^32 - 141293760628767613706513088413804332516295504*T7^31 + 140321115837403727116817630046630340688151656*T7^30 - 34329265117937665397559152986580295791067468*T7^29 - 163375654313300765588816367478736915234080325*T7^28 + 392658959878735845344380871896485986198835368*T7^27 - 522708448175637753280431597904318109607837152*T7^26 + 472310600043978375075260199677668760792781388*T7^25 - 138038607928831129281898684860215469326545647*T7^24 - 327881698531043688061341348008383729145109844*T7^23 + 885058275365776396235834530974786791942871086*T7^22 - 1262031201286319212319246775296533772157616892*T7^21 + 1413788995953109877649583343183205906705845478*T7^20 - 1264475572952428777513636901580588380541961880*T7^19 + 1008853482809159030159545017216801990313172524*T7^18 - 640874603362946982168119323353291917968111304*T7^17 + 401509191267335834095276390732666307012641321*T7^16 - 171347600950856139326191506225819758500190020*T7^15 + 85955030451862420537071069681157432232270200*T7^14 - 13218070588816644610597151302915047980204808*T7^13 + 14147949342888446322809023053070816621058492*T7^12 + 4835405795403993544971910455228319805421648*T7^11 + 10240512225560636330244630745182798580795712*T7^10 + 5500636763018317285170640985710258707544384*T7^9 + 5986509429830092668476320003790205646644624*T7^8 + 3460643188813572525441067622548062102933888*T7^7 + 2034998366034595353791784190377901834158848*T7^6 + 878316138717180656735750392116461882450560*T7^5 + 314369699864352633269543076251235539124160*T7^4 + 85789321114937811320801262418740250196736*T7^3 + 19222451478713770485674674275451230678528*T7^2 + 2616250016028775292361291548982562430464*T7 + 344148528744680629897567854960054866176 acting on $S_{2}^{\mathrm{new}}(930, [\chi])$.

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:	\( N \)	\(=\)	\( 930 = 2 \cdot 3 \cdot 5 \cdot 31 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	930.bj (of order \(20\), degree \(8\), minimal)

\(n\):		e.g. 2-40 or 990-1000
Embeddings:		e.g. 1-3 or 277.16
Significant digits:
Format:

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