LMFDB - Newform orbit 354.2.e.c

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [354,2,Mod(7,354)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(354, base_ring=CyclotomicField(58))

chi = DirichletCharacter(H, H._module([0, 18]))

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

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

chi := DirichletCharacter("354.7");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 354 = 2 \cdot 3 \cdot 59 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	354.e (of order $29$, degree $28$, 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:	$2.82670423155$
Analytic rank:	$0$
Dimension:	$84$
Relative dimension:	$3$ over $\Q(\zeta_{29})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{29}]$

$q$-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) = $ $ 84 q - 3 q^{2} + 3 q^{3} - 3 q^{4} + 3 q^{6} + q^{7} - 3 q^{8} - 3 q^{9}+O(q^{10}) $

$\operatorname{Tr}(f)(q) = $ $ 84 q - 3 q^{2} + 3 q^{3} - 3 q^{4} + 3 q^{6} + q^{7} - 3 q^{8} - 3 q^{9} - 26 q^{11} + 3 q^{12} - 3 q^{13} + q^{14} - 3 q^{16} + 3 q^{17} - 3 q^{18} + 4 q^{19} - q^{21} + 3 q^{22} - 2 q^{23} + 3 q^{24} + 41 q^{25} + 26 q^{26} + 3 q^{27} + q^{28} - 2 q^{29} + 8 q^{31} - 3 q^{32} - 3 q^{33} - 26 q^{34} + 83 q^{35} - 3 q^{36} - 53 q^{37} + 4 q^{38} + 3 q^{39} - 7 q^{41} - q^{42} + 119 q^{43} + 3 q^{44} - 31 q^{46} - 12 q^{47} + 3 q^{48} - 38 q^{49} - 133 q^{50} - 3 q^{51} - 32 q^{52} - 83 q^{53} + 3 q^{54} - 83 q^{55} + q^{56} - 4 q^{57} + 56 q^{58} - 57 q^{59} - 48 q^{61} - 21 q^{62} + q^{63} - 3 q^{64} - 33 q^{65} - 3 q^{66} - 88 q^{67} - 26 q^{68} + 89 q^{69} - 62 q^{70} - 35 q^{71} - 3 q^{72} - 71 q^{73} - 24 q^{74} + 17 q^{75} + 33 q^{76} + 113 q^{77} + 3 q^{78} - 5 q^{79} - 3 q^{81} - 7 q^{82} - 51 q^{83} - q^{84} + 125 q^{85} + 61 q^{86} + 31 q^{87} + 32 q^{88} - 58 q^{89} + 173 q^{91} - 2 q^{92} + 21 q^{93} + 17 q^{94} + 26 q^{95} + 3 q^{96} + 20 q^{98} + 3 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} $
7.1	−0.561187	−	0.827689i	−0.0541389	+	0.998533i	−0.370138	+	0.928977i	−3.82834	+	1.77118i	0.856857	−	0.515554i	1.02375	−	3.68721i	0.976621	−	0.214970i	−0.994138	−	0.108119i	3.61440	+	2.17471i
7.2	−0.561187	−	0.827689i	−0.0541389	+	0.998533i	−0.370138	+	0.928977i	−0.0493609	+	0.0228368i	0.856857	−	0.515554i	−0.676801	+	2.43762i	0.976621	−	0.214970i	−0.994138	−	0.108119i	0.0466025	+	0.0280398i
7.3	−0.561187	−	0.827689i	−0.0541389	+	0.998533i	−0.370138	+	0.928977i	3.87770	−	1.79401i	0.856857	−	0.515554i	0.929941	−	3.34934i	0.976621	−	0.214970i	−0.994138	−	0.108119i	−3.66100	−	2.20275i
19.1	0.468408	−	0.883512i	0.725995	−	0.687699i	−0.561187	−	0.827689i	−3.74342	+	0.823990i	−0.267528	−	0.963550i	−3.11942	+	2.37132i	−0.994138	+	0.108119i	0.0541389	−	0.998533i	−1.02545	+	3.69332i
19.2	0.468408	−	0.883512i	0.725995	−	0.687699i	−0.561187	−	0.827689i	1.70467	−	0.375225i	−0.267528	−	0.963550i	1.66436	−	1.26521i	−0.994138	+	0.108119i	0.0541389	−	0.998533i	0.466964	−	1.68185i
19.3	0.468408	−	0.883512i	0.725995	−	0.687699i	−0.561187	−	0.827689i	2.03876	−	0.448764i	−0.267528	−	0.963550i	−0.284870	+	0.216552i	−0.994138	+	0.108119i	0.0541389	−	0.998533i	0.558482	−	2.01147i
25.1	0.796093	+	0.605174i	−0.468408	−	0.883512i	0.267528	+	0.963550i	−2.86336	−	2.71232i	0.161782	−	0.986827i	−2.64683	+	3.11609i	−0.370138	+	0.928977i	−0.561187	+	0.827689i	−0.638077	−	3.89210i
25.2	0.796093	+	0.605174i	−0.468408	−	0.883512i	0.267528	+	0.963550i	0.697351	+	0.660566i	0.161782	−	0.986827i	−1.30774	+	1.53959i	−0.370138	+	0.928977i	−0.561187	+	0.827689i	0.155399	+	0.947890i
25.3	0.796093	+	0.605174i	−0.468408	−	0.883512i	0.267528	+	0.963550i	2.16601	+	2.05176i	0.161782	−	0.986827i	2.55368	−	3.00642i	−0.370138	+	0.928977i	−0.561187	+	0.827689i	0.482678	+	2.94421i
49.1	−0.370138	+	0.928977i	0.994138	+	0.108119i	−0.725995	−	0.687699i	−1.72394	+	2.02958i	−0.468408	+	0.883512i	−1.98744	−	1.19580i	0.907575	−	0.419889i	0.976621	+	0.214970i	−1.24733	−	2.35272i
49.2	−0.370138	+	0.928977i	0.994138	+	0.108119i	−0.725995	−	0.687699i	0.271121	−	0.319189i	−0.468408	+	0.883512i	3.97639	+	2.39251i	0.907575	−	0.419889i	0.976621	+	0.214970i	0.196166	+	0.370009i
49.3	−0.370138	+	0.928977i	0.994138	+	0.108119i	−0.725995	−	0.687699i	1.45282	−	1.71039i	−0.468408	+	0.883512i	−1.71569	−	1.03229i	0.907575	−	0.419889i	0.976621	+	0.214970i	1.05117	+	1.98271i
79.1	0.907575	+	0.419889i	0.947653	−	0.319302i	0.647386	+	0.762162i	−2.35642	+	1.41781i	0.994138	+	0.108119i	0.260327	+	4.80144i	0.267528	+	0.963550i	0.796093	−	0.605174i	−2.73396	+	0.297336i
79.2	0.907575	+	0.419889i	0.947653	−	0.319302i	0.647386	+	0.762162i	0.401618	−	0.241646i	0.994138	+	0.108119i	−0.0924092	−	1.70439i	0.267528	+	0.963550i	0.796093	−	0.605174i	0.465963	−	0.0506766i
79.3	0.907575	+	0.419889i	0.947653	−	0.319302i	0.647386	+	0.762162i	1.95481	−	1.17617i	0.994138	+	0.108119i	0.00134066	+	0.0247270i	0.267528	+	0.963550i	0.796093	−	0.605174i	2.26799	−	0.246659i
85.1	0.796093	−	0.605174i	−0.468408	+	0.883512i	0.267528	−	0.963550i	−2.86336	+	2.71232i	0.161782	+	0.986827i	−2.64683	−	3.11609i	−0.370138	−	0.928977i	−0.561187	−	0.827689i	−0.638077	+	3.89210i
85.2	0.796093	−	0.605174i	−0.468408	+	0.883512i	0.267528	−	0.963550i	0.697351	−	0.660566i	0.161782	+	0.986827i	−1.30774	−	1.53959i	−0.370138	−	0.928977i	−0.561187	−	0.827689i	0.155399	−	0.947890i
85.3	0.796093	−	0.605174i	−0.468408	+	0.883512i	0.267528	−	0.963550i	2.16601	−	2.05176i	0.161782	+	0.986827i	2.55368	+	3.00642i	−0.370138	−	0.928977i	−0.561187	−	0.827689i	0.482678	−	2.94421i
121.1	0.907575	−	0.419889i	0.947653	+	0.319302i	0.647386	−	0.762162i	−2.35642	−	1.41781i	0.994138	−	0.108119i	0.260327	−	4.80144i	0.267528	−	0.963550i	0.796093	+	0.605174i	−2.73396	−	0.297336i
121.2	0.907575	−	0.419889i	0.947653	+	0.319302i	0.647386	−	0.762162i	0.401618	+	0.241646i	0.994138	−	0.108119i	−0.0924092	+	1.70439i	0.267528	−	0.963550i	0.796093	+	0.605174i	0.465963	+	0.0506766i

See all 84 embeddings

Inner twists

Char	Parity	Ord	Mult	Type
1.a	even	1	1	trivial
59.c	even	29	1	inner

Twists

By twisting character orbit
Char	Parity	Ord	Mult	Type	Twist	Min	Dim
1.a	even	1	1	trivial	354.2.e.c	✓	84
59.c	even	29	1	inner	354.2.e.c	✓	84

By twisted newform orbit
Twist	Min	Dim	Char	Parity	Ord	Mult	Type
354.2.e.c	✓	84	1.a	even	1	1	trivial
354.2.e.c	✓	84	59.c	even	29	1	inner

Hecke kernels

This newform subspace can be constructed as the kernel of the linear operator $ T_{5}^{84} - 13 T_{5}^{82} + 29 T_{5}^{81} + 198 T_{5}^{80} + 355 T_{5}^{78} - 1276 T_{5}^{77} + \cdots + 35473828792081 $ T5^84 - 13*T5^82 + 29*T5^81 + 198*T5^80 + 355*T5^78 - 1276*T5^77 + 49325*T5^76 + 202014*T5^75 - 450289*T5^74 - 1048263*T5^73 + 15342354*T5^72 + 5513654*T5^71 - 227873096*T5^70 + 524677164*T5^69 + 2132912171*T5^68 - 7737029277*T5^67 - 8300797199*T5^66 - 10095552471*T5^65 + 235394700190*T5^64 - 449355803271*T5^63 - 404144878501*T5^62 + 9170761472264*T5^61 - 28193667654359*T5^60 + 33056645338493*T5^59 + 62344214823457*T5^58 - 88482192687604*T5^57 - 1523167648497332*T5^56 - 273443122870180*T5^55 + 20661079932300803*T5^54 - 37817249465165561*T5^53 - 45265723233506294*T5^52 - 135967622650910614*T5^51 + 1252414180000997621*T5^50 - 1799530004172675580*T5^49 + 14633562579356981177*T5^48 - 38411557011792971366*T5^47 + 35928217052816234778*T5^46 - 170322789484325989991*T5^45 + 819428103553831171517*T5^44 - 2018783611647027704341*T5^43 + 5393566347145738479463*T5^42 - 13600674400982089529154*T5^41 + 31911537090491894911348*T5^40 - 116011588457360334278280*T5^39 + 405020012375535659679885*T5^38 - 993027436844198060232009*T5^37 + 2061488395562503207364723*T5^36 - 4595230844326043861583605*T5^35 + 10417127457509399023887543*T5^34 - 25368149931300631082802270*T5^33 + 64131853824711833663918852*T5^32 - 123331344646476439732484093*T5^31 + 181212047810740601784767905*T5^30 - 253893002235303018524257516*T5^29 + 352890790909035943534824449*T5^28 - 478696343449191488240700115*T5^27 + 622023873706648683003485779*T5^26 - 728117547378941745067455533*T5^25 + 845307303849513436024136117*T5^24 - 894975308817101847831360509*T5^23 + 872846859023268702438684352*T5^22 - 756215924297675525220317848*T5^21 + 621730725197599829772354352*T5^20 - 452079501531433212218121219*T5^19 + 287868214285789486517821906*T5^18 - 158997303791462708443000798*T5^17 + 68159458738255622633486987*T5^16 - 18486597903169355355461966*T5^15 + 435375440037037741402330*T5^14 + 2124506318463150172614470*T5^13 - 843283618130020207592307*T5^12 + 8326642741261381399063*T5^11 + 107620631676867193995879*T5^10 - 43817870451669580619587*T5^9 + 9801981054273550573780*T5^8 - 1745287376318541276544*T5^7 + 395940280368963267466*T5^6 + 7211941364354946853*T5^5 + 11969263302592392060*T5^4 + 1679008807570833232*T5^3 + 91372545582451038*T5^2 + 2250616227730850*T5 + 35473828792081 acting on $S_{2}^{\mathrm{new}}(354, [\chi])$.

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:	\( N \)	\(=\)	\( 354 = 2 \cdot 3 \cdot 59 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	354.e (of order \(29\), degree \(28\), minimal)

\(n\):		e.g. 2-40 or 990-1000
Embeddings:		e.g. 1-3 or 7.3
Significant digits:
Format:

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more