LMFDB - Newform orbit 930.2.bn.b

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [930,2,Mod(19,930)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(930, base_ring=CyclotomicField(30))

chi = DirichletCharacter(H, H._module([0, 15, 4]))

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

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

chi := DirichletCharacter("930.19");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 930 = 2 \cdot 3 \cdot 5 \cdot 31 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	930.bn (of order $30$, 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:	$144$
Relative dimension:	$18$ over $\Q(\zeta_{30})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{30}]$

$q$-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) = $ $ 144 q + 36 q^{4} + 2 q^{5} - 72 q^{6} - 18 q^{9}+O(q^{10}) $

$\operatorname{Tr}(f)(q) = $ $ 144 q + 36 q^{4} + 2 q^{5} - 72 q^{6} - 18 q^{9} - 18 q^{11} - 8 q^{14} - 36 q^{16} - 24 q^{19} - 2 q^{20} + 28 q^{21} - 18 q^{24} + 10 q^{25} - 12 q^{26} - 4 q^{30} - 4 q^{31} + 10 q^{34} - 2 q^{35} - 72 q^{36} + 16 q^{39} + 4 q^{41} - 2 q^{44} - 2 q^{45} - 2 q^{46} - 78 q^{49} + 32 q^{50} + 10 q^{51} + 36 q^{54} - 50 q^{55} - 12 q^{56} + 28 q^{59} + 88 q^{61} + 36 q^{64} - 124 q^{65} + 6 q^{66} - 46 q^{69} - 10 q^{70} + 140 q^{71} + 34 q^{74} - 32 q^{75} + 24 q^{76} + 16 q^{79} + 12 q^{80} + 18 q^{81} - 8 q^{84} + 74 q^{85} - 98 q^{86} + 148 q^{89} + 44 q^{91} - 108 q^{94} - 80 q^{95} + 18 q^{96} - 2 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_{6} $			$ a_{7} $			$ a_{8} $			$ a_{9} $			$ a_{10} $
19.1	−0.587785	+	0.809017i	−0.406737	+	0.913545i	−0.309017	−	0.951057i	−1.89205	−	1.19170i	−0.500000	−	0.866025i	−1.93366	−	1.74107i	0.951057	+	0.309017i	−0.669131	−	0.743145i	2.07622	−	0.830237i
19.2	−0.587785	+	0.809017i	−0.406737	+	0.913545i	−0.309017	−	0.951057i	−1.39553	+	1.74714i	−0.500000	−	0.866025i	1.99915	+	1.80004i	0.951057	+	0.309017i	−0.669131	−	0.743145i	−0.593198	−	2.15595i
19.3	−0.587785	+	0.809017i	−0.406737	+	0.913545i	−0.309017	−	0.951057i	−1.16157	−	1.91070i	−0.500000	−	0.866025i	2.15311	+	1.93867i	0.951057	+	0.309017i	−0.669131	−	0.743145i	2.22854	+	0.183353i
19.4	−0.587785	+	0.809017i	−0.406737	+	0.913545i	−0.309017	−	0.951057i	−0.978641	+	2.01054i	−0.500000	−	0.866025i	−2.38970	−	2.15169i	0.951057	+	0.309017i	−0.669131	−	0.743145i	−1.05133	−	1.97350i
19.5	−0.587785	+	0.809017i	−0.406737	+	0.913545i	−0.309017	−	0.951057i	−0.293219	−	2.21676i	−0.500000	−	0.866025i	1.44492	+	1.30102i	0.951057	+	0.309017i	−0.669131	−	0.743145i	1.96575	+	1.06576i
19.6	−0.587785	+	0.809017i	−0.406737	+	0.913545i	−0.309017	−	0.951057i	0.991216	+	2.00437i	−0.500000	−	0.866025i	0.807100	+	0.726716i	0.951057	+	0.309017i	−0.669131	−	0.743145i	−2.20419	−	0.376228i
19.7	−0.587785	+	0.809017i	−0.406737	+	0.913545i	−0.309017	−	0.951057i	1.47304	−	1.68231i	−0.500000	−	0.866025i	−2.98158	−	2.68462i	0.951057	+	0.309017i	−0.669131	−	0.743145i	0.495182	+	2.18055i
19.8	−0.587785	+	0.809017i	−0.406737	+	0.913545i	−0.309017	−	0.951057i	2.02048	−	0.957953i	−0.500000	−	0.866025i	1.95080	+	1.75650i	0.951057	+	0.309017i	−0.669131	−	0.743145i	−0.412606	+	2.19767i
19.9	−0.587785	+	0.809017i	−0.406737	+	0.913545i	−0.309017	−	0.951057i	2.14981	+	0.615060i	−0.500000	−	0.866025i	−2.84716	−	2.56360i	0.951057	+	0.309017i	−0.669131	−	0.743145i	−1.76122	+	1.37771i
19.10	0.587785	−	0.809017i	0.406737	−	0.913545i	−0.309017	−	0.951057i	−2.23144	+	0.143766i	−0.500000	−	0.866025i	−0.807100	−	0.726716i	−0.951057	−	0.309017i	−0.669131	−	0.743145i	−1.19530	+	1.88978i
19.11	0.587785	−	0.809017i	0.406737	−	0.913545i	−0.309017	−	0.951057i	−1.60756	−	1.55426i	−0.500000	−	0.866025i	2.84716	+	2.56360i	−0.951057	−	0.309017i	−0.669131	−	0.743145i	−2.20233	+	0.386974i
19.12	0.587785	−	0.809017i	0.406737	−	0.913545i	−0.309017	−	0.951057i	−1.25186	+	1.85280i	−0.500000	−	0.866025i	2.38970	+	2.15169i	−0.951057	−	0.309017i	−0.669131	−	0.743145i	0.763121	+	2.10182i
19.13	0.587785	−	0.809017i	0.406737	−	0.913545i	−0.309017	−	0.951057i	−0.815306	+	2.08213i	−0.500000	−	0.866025i	−1.99915	−	1.80004i	−0.951057	−	0.309017i	−0.669131	−	0.743145i	1.20526	+	1.88344i
19.14	0.587785	−	0.809017i	0.406737	−	0.913545i	−0.309017	−	0.951057i	−0.180627	−	2.22876i	−0.500000	−	0.866025i	−1.95080	−	1.75650i	−0.951057	−	0.309017i	−0.669131	−	0.743145i	−1.90927	−	1.16390i
19.15	0.587785	−	0.809017i	0.406737	−	0.913545i	−0.309017	−	0.951057i	0.720399	−	2.11684i	−0.500000	−	0.866025i	2.98158	+	2.68462i	−0.951057	−	0.309017i	−0.669131	−	0.743145i	−1.28912	−	1.82706i
19.16	0.587785	−	0.809017i	0.406737	−	0.913545i	−0.309017	−	0.951057i	1.97807	+	1.04271i	−0.500000	−	0.866025i	1.93366	+	1.74107i	−0.951057	−	0.309017i	−0.669131	−	0.743145i	2.00625	−	0.987398i
19.17	0.587785	−	0.809017i	0.406737	−	0.913545i	−0.309017	−	0.951057i	2.06638	−	0.854445i	−0.500000	−	0.866025i	−1.44492	−	1.30102i	−0.951057	−	0.309017i	−0.669131	−	0.743145i	0.523327	−	2.17397i
19.18	0.587785	−	0.809017i	0.406737	−	0.913545i	−0.309017	−	0.951057i	2.23550	+	0.0505968i	−0.500000	−	0.866025i	−2.15311	−	1.93867i	−0.951057	−	0.309017i	−0.669131	−	0.743145i	1.35492	−	1.77881i
49.1	−0.587785	−	0.809017i	−0.406737	−	0.913545i	−0.309017	+	0.951057i	−1.89205	+	1.19170i	−0.500000	+	0.866025i	−1.93366	+	1.74107i	0.951057	−	0.309017i	−0.669131	+	0.743145i	2.07622	+	0.830237i
49.2	−0.587785	−	0.809017i	−0.406737	−	0.913545i	−0.309017	+	0.951057i	−1.39553	−	1.74714i	−0.500000	+	0.866025i	1.99915	−	1.80004i	0.951057	−	0.309017i	−0.669131	+	0.743145i	−0.593198	+	2.15595i

See next 80 embeddings (of 144 total)

Inner twists

Char	Parity	Ord	Mult	Type
1.a	even	1	1	trivial
5.b	even	2	1	inner
31.g	even	15	1	inner
155.u	even	30	1	inner

Twists

By twisting character orbit
Char	Parity	Ord	Mult	Type	Twist	Min	Dim
1.a	even	1	1	trivial	930.2.bn.b	✓	144
5.b	even	2	1	inner	930.2.bn.b	✓	144
31.g	even	15	1	inner	930.2.bn.b	✓	144
155.u	even	30	1	inner	930.2.bn.b	✓	144

By twisted newform orbit
Twist	Min	Dim	Char	Parity	Ord	Mult	Type
930.2.bn.b	✓	144	1.a	even	1	1	trivial
930.2.bn.b	✓	144	5.b	even	2	1	inner
930.2.bn.b	✓	144	31.g	even	15	1	inner
930.2.bn.b	✓	144	155.u	even	30	1	inner

Hecke kernels

This newform subspace can be constructed as the kernel of the linear operator $ T_{7}^{144} + 102 T_{7}^{142} + 4183 T_{7}^{140} + 53720 T_{7}^{138} - 1977413 T_{7}^{136} + \cdots + 11\!\cdots\!56 $ T7^144 + 102*T7^142 + 4183*T7^140 + 53720*T7^138 - 1977413*T7^136 - 99109344*T7^134 - 1530919115*T7^132 + 9459188784*T7^130 + 882801412180*T7^128 + 18180667097914*T7^126 + 141275403892931*T7^124 - 2800382440955352*T7^122 - 112495170620037495*T7^120 - 1680126457385506910*T7^118 - 5065895617903058844*T7^116 + 282553085672181938408*T7^114 + 7005087005411739965730*T7^112 + 79792000912179938227282*T7^110 + 210663155414966028431910*T7^108 - 11244158616467596703584698*T7^106 - 214700306180372038112479067*T7^104 - 1894827488212562419827290336*T7^102 - 1095332312880673879446784320*T7^100 + 213637356115176868166292085830*T7^98 + 3598953894745092225471833720683*T7^96 + 27207961589117378051200041344658*T7^94 + 18459797433598250127533141618833*T7^92 - 2446130157403489278090679482555472*T7^90 - 32301991357537916413034678904852600*T7^88 - 245512112976494446452282466712444086*T7^86 - 337194177982129852092201120315632537*T7^84 + 13576322350790270209545973801649901472*T7^82 + 192258180162631888072678208257637898946*T7^80 + 1314832786595419281795244612346371718860*T7^78 + 4599723686434956653895898497004420466255*T7^76 - 30400692020721323568192938062014700810722*T7^74 - 525418765717072054676099197098997261707809*T7^72 - 4081602438969773403564008143056380515345386*T7^70 - 14192986329623960271808366717600106550058860*T7^68 + 3632616539805876674446006213533881203942066*T7^66 + 824208421812946902704616395688188146517164903*T7^64 + 6567647656488974218505123125663798482209032400*T7^62 + 31506764140600814165291714160358043022312375467*T7^60 + 83540692226712524434966785236657148361459928420*T7^58 + 11083891713248203025777180866666912669250724422*T7^56 - 2736217909024668409499593104943474997277140049930*T7^54 - 7619941424773539120315899970421427020079889011462*T7^52 - 25456295414471812879453657151523052940905633173174*T7^50 + 63320651709906103053523910232490084448170356684825*T7^48 + 219181631053236225520565454192400683995799148646772*T7^46 + 1742137744102053890988739656260566460548509818467225*T7^44 + 255855917694526243039686043102297429558853350252548*T7^42 - 3054266226437143142305397211174020063158610614827904*T7^40 - 28721880573993286166743779376918885685680807153652630*T7^38 + 13592455403366539951958540878037400772173200100711967*T7^36 + 12617741624492840893279428868625236006697860129301850*T7^34 + 88922174366409060995703900731056491952750774774404518*T7^32 + 114533432303950068604275009957635411498130569057736*T7^30 + 105419605947965865216710989182608751717859908050283840*T7^28 - 73875447774459333526649463344172401810916688380803998*T7^26 - 33322389844561748374885768120815202417564662803792647*T7^24 + 4751245915356379200249383154549322614803621461667064*T7^22 + 6782113919947036108200199672819814227222725109801130*T7^20 + 1951875033855687954236593738056606178543366758534360*T7^18 + 265577789655015525610750036507914600169592232602753*T7^16 + 17775009157795517435588619952648289792554255247728*T7^14 + 608418859437014903865106487152634168094444647168*T7^12 + 10060597882108891837604123611763588628512186368*T7^10 + 85283633257419129379303939278061718618439680*T7^8 + 346883075165209816086068716309029232574464*T7^6 + 459412875067103332066564178126493974528*T7^4 - 528422635356308149563989494929031168*T7^2 + 119961435612561189036937084665856 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.bn (of order \(30\), degree \(8\), minimal)

\(n\):		e.g. 2-40 or 990-1000
Embeddings:		e.g. 1-3 or 19.18
Significant digits:
Format:

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