LMFDB - Newform orbit 354.2.e.d

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} - 2 q^{5} + 3 q^{6} - 7 q^{7} + 3 q^{8} - 3 q^{9}+O(q^{10}) $

$\operatorname{Tr}(f)(q) = $ \( 84 q + 3 q^{2} - 3 q^{3} - 3 q^{4} - 2 q^{5} + 3 q^{6} - 7 q^{7} + 3 q^{8} - 3 q^{9} + 2 q^{10} + 30 q^{11} - 3 q^{12} - 3 q^{13} + 7 q^{14} - 2 q^{15} - 3 q^{16} + 3 q^{17} + 3 q^{18} - 4 q^{19} - 2 q^{20} - 7 q^{21} - q^{22} + 2 q^{23} + 3 q^{24} - 67 q^{25} + 32 q^{26} - 3 q^{27} - 7 q^{28} + 4 q^{29} + 2 q^{30} - 6 q^{31} + 3 q^{32} + q^{33} + 26 q^{34} + 79 q^{35} - 3 q^{36} + 55 q^{37} + 4 q^{38} - 3 q^{39} + 2 q^{40} + q^{41} + 7 q^{42} + 51 q^{43} + q^{44} - 2 q^{45} - 31 q^{46} - 62 q^{47} - 3 q^{48} - 70 q^{49} + 9 q^{50} + 3 q^{51} - 32 q^{52} - 27 q^{53} + 3 q^{54} - 83 q^{55} + 7 q^{56} - 4 q^{57} - 120 q^{58} - 55 q^{59} + 56 q^{60} - 46 q^{61} - 23 q^{62} - 7 q^{63} - 3 q^{64} - 121 q^{65} - q^{66} + 8 q^{67} - 26 q^{68} - 27 q^{69} - 50 q^{70} - 61 q^{71} + 3 q^{72} + 49 q^{73} - 26 q^{74} - 9 q^{75} + 25 q^{76} + 77 q^{77} + 3 q^{78} - 5 q^{79} - 2 q^{80} - 3 q^{81} - q^{82} + 75 q^{83} - 7 q^{84} + 189 q^{85} + 65 q^{86} - 25 q^{87} - 30 q^{88} + 54 q^{89} + 2 q^{90} - 161 q^{91} + 2 q^{92} + 23 q^{93} + 33 q^{94} - 54 q^{95} + 3 q^{96} + 28 q^{97} + 12 q^{98} + q^{99}+O(q^{100}) \)

84 * q + 3 * q^2 - 3 * q^3 - 3 * q^4 - 2 * q^5 + 3 * q^6 - 7 * q^7 + 3 * q^8 - 3 * q^9 + 2 * q^10 + 30 * q^11 - 3 * q^12 - 3 * q^13 + 7 * q^14 - 2 * q^15 - 3 * q^16 + 3 * q^17 + 3 * q^18 - 4 * q^19 - 2 * q^20 - 7 * q^21 - q^22 + 2 * q^23 + 3 * q^24 - 67 * q^25 + 32 * q^26 - 3 * q^27 - 7 * q^28 + 4 * q^29 + 2 * q^30 - 6 * q^31 + 3 * q^32 + q^33 + 26 * q^34 + 79 * q^35 - 3 * q^36 + 55 * q^37 + 4 * q^38 - 3 * q^39 + 2 * q^40 + q^41 + 7 * q^42 + 51 * q^43 + q^44 - 2 * q^45 - 31 * q^46 - 62 * q^47 - 3 * q^48 - 70 * q^49 + 9 * q^50 + 3 * q^51 - 32 * q^52 - 27 * q^53 + 3 * q^54 - 83 * q^55 + 7 * q^56 - 4 * q^57 - 120 * q^58 - 55 * q^59 + 56 * q^60 - 46 * q^61 - 23 * q^62 - 7 * q^63 - 3 * q^64 - 121 * q^65 - q^66 + 8 * q^67 - 26 * q^68 - 27 * q^69 - 50 * q^70 - 61 * q^71 + 3 * q^72 + 49 * q^73 - 26 * q^74 - 9 * q^75 + 25 * q^76 + 77 * q^77 + 3 * q^78 - 5 * q^79 - 2 * q^80 - 3 * q^81 - q^82 + 75 * q^83 - 7 * q^84 + 189 * q^85 + 65 * q^86 - 25 * q^87 - 30 * q^88 + 54 * q^89 + 2 * q^90 - 161 * q^91 + 2 * q^92 + 23 * q^93 + 33 * q^94 - 54 * q^95 + 3 * q^96 + 28 * q^97 + 12 * q^98 + 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} $
7.1	0.561187	+	0.827689i	0.0541389	−	0.998533i	−0.370138	+	0.928977i	−1.35846	+	0.628489i	0.856857	−	0.515554i	−1.22687	+	4.41877i	−0.976621	+	0.214970i	−0.994138	−	0.108119i	−1.28254	−	0.771679i
7.2	0.561187	+	0.827689i	0.0541389	−	0.998533i	−0.370138	+	0.928977i	−0.147621	+	0.0682969i	0.856857	−	0.515554i	1.13460	−	4.08646i	−0.976621	+	0.214970i	−0.994138	−	0.108119i	−0.139372	−	0.0838572i
7.3	0.561187	+	0.827689i	0.0541389	−	0.998533i	−0.370138	+	0.928977i	3.32123	−	1.53656i	0.856857	−	0.515554i	−0.148313	+	0.534175i	−0.976621	+	0.214970i	−0.994138	−	0.108119i	3.13563	+	1.88664i
19.1	−0.468408	+	0.883512i	−0.725995	+	0.687699i	−0.561187	−	0.827689i	−0.363688	+	0.0800537i	−0.267528	−	0.963550i	2.14232	−	1.62855i	0.994138	−	0.108119i	0.0541389	−	0.998533i	0.0996260	−	0.358820i
19.2	−0.468408	+	0.883512i	−0.725995	+	0.687699i	−0.561187	−	0.827689i	−0.307038	+	0.0675842i	−0.267528	−	0.963550i	−2.91202	+	2.21366i	0.994138	−	0.108119i	0.0541389	−	0.998533i	0.0841078	−	0.302929i
19.3	−0.468408	+	0.883512i	−0.725995	+	0.687699i	−0.561187	−	0.827689i	2.62397	−	0.577579i	−0.267528	−	0.963550i	1.37326	−	1.04393i	0.994138	−	0.108119i	0.0541389	−	0.998533i	−0.718790	+	2.58885i
25.1	−0.796093	−	0.605174i	0.468408	+	0.883512i	0.267528	+	0.963550i	−3.02590	−	2.86629i	0.161782	−	0.986827i	−1.62278	+	1.91048i	0.370138	−	0.928977i	−0.561187	+	0.827689i	0.674297	+	4.11303i
25.2	−0.796093	−	0.605174i	0.468408	+	0.883512i	0.267528	+	0.963550i	−0.526198	−	0.498441i	0.161782	−	0.986827i	2.82058	−	3.32064i	0.370138	−	0.928977i	−0.561187	+	0.827689i	0.117259	+	0.715246i
25.3	−0.796093	−	0.605174i	0.468408	+	0.883512i	0.267528	+	0.963550i	2.10011	+	1.98933i	0.161782	−	0.986827i	−0.956124	+	1.12564i	0.370138	−	0.928977i	−0.561187	+	0.827689i	−0.467991	−	2.85462i
49.1	0.370138	−	0.928977i	−0.994138	−	0.108119i	−0.725995	−	0.687699i	−1.43265	+	1.68664i	−0.468408	+	0.883512i	−0.808791	−	0.486633i	−0.907575	+	0.419889i	0.976621	+	0.214970i	1.03657	+	1.95519i
49.2	0.370138	−	0.928977i	−0.994138	−	0.108119i	−0.725995	−	0.687699i	0.645875	−	0.760383i	−0.468408	+	0.883512i	4.24666	+	2.55513i	−0.907575	+	0.419889i	0.976621	+	0.214970i	−0.467315	−	0.881449i
49.3	0.370138	−	0.928977i	−0.994138	−	0.108119i	−0.725995	−	0.687699i	2.08155	−	2.45058i	−0.468408	+	0.883512i	−3.50142	−	2.10673i	−0.907575	+	0.419889i	0.976621	+	0.214970i	−1.50608	−	2.84076i
79.1	−0.907575	−	0.419889i	−0.947653	+	0.319302i	0.647386	+	0.762162i	−3.13475	+	1.88612i	0.994138	+	0.108119i	0.104895	+	1.93468i	−0.267528	−	0.963550i	0.796093	−	0.605174i	3.63698	−	0.395546i
79.2	−0.907575	−	0.419889i	−0.947653	+	0.319302i	0.647386	+	0.762162i	−0.971226	+	0.584367i	0.994138	+	0.108119i	−0.0967973	−	1.78532i	−0.267528	−	0.963550i	0.796093	−	0.605174i	1.12683	−	0.122550i
79.3	−0.907575	−	0.419889i	−0.947653	+	0.319302i	0.647386	+	0.762162i	2.39226	−	1.43938i	0.994138	+	0.108119i	0.142415	+	2.62669i	−0.267528	−	0.963550i	0.796093	−	0.605174i	−2.77554	+	0.301858i
85.1	−0.796093	+	0.605174i	0.468408	−	0.883512i	0.267528	−	0.963550i	−3.02590	+	2.86629i	0.161782	+	0.986827i	−1.62278	−	1.91048i	0.370138	+	0.928977i	−0.561187	−	0.827689i	0.674297	−	4.11303i
85.2	−0.796093	+	0.605174i	0.468408	−	0.883512i	0.267528	−	0.963550i	−0.526198	+	0.498441i	0.161782	+	0.986827i	2.82058	+	3.32064i	0.370138	+	0.928977i	−0.561187	−	0.827689i	0.117259	−	0.715246i
85.3	−0.796093	+	0.605174i	0.468408	−	0.883512i	0.267528	−	0.963550i	2.10011	−	1.98933i	0.161782	+	0.986827i	−0.956124	−	1.12564i	0.370138	+	0.928977i	−0.561187	−	0.827689i	−0.467991	+	2.85462i
121.1	−0.907575	+	0.419889i	−0.947653	−	0.319302i	0.647386	−	0.762162i	−3.13475	−	1.88612i	0.994138	−	0.108119i	0.104895	−	1.93468i	−0.267528	+	0.963550i	0.796093	+	0.605174i	3.63698	+	0.395546i
121.2	−0.907575	+	0.419889i	−0.947653	−	0.319302i	0.647386	−	0.762162i	−0.971226	−	0.584367i	0.994138	−	0.108119i	−0.0967973	+	1.78532i	−0.267528	+	0.963550i	0.796093	+	0.605174i	1.12683	+	0.122550i

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.d	✓	84
59.c	even	29	1	inner	354.2.e.d	✓	84

By twisted newform orbit
Twist	Min	Dim	Char	Parity	Ord	Mult	Type
354.2.e.d	✓	84	1.a	even	1	1	trivial
354.2.e.d	✓	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} + 2 T_{5}^{83} + 43 T_{5}^{82} + 135 T_{5}^{81} + 1048 T_{5}^{80} + 3736 T_{5}^{79} + \cdots + 21\!\cdots\!61 $ T5^84 + 2*T5^83 + 43*T5^82 + 135*T5^81 + 1048*T5^80 + 3736*T5^79 + 20011*T5^78 + 67580*T5^77 + 296265*T5^76 + 1227614*T5^75 + 4110529*T5^74 + 20504883*T5^73 + 64956684*T5^72 + 276737042*T5^71 + 959638936*T5^70 + 3697789704*T5^69 + 11800681581*T5^68 + 44205681127*T5^67 + 136930795823*T5^66 + 436820556689*T5^65 + 1669601867126*T5^64 + 3909078989123*T5^63 + 18680789077715*T5^62 + 38826093513928*T5^61 + 185522511465525*T5^60 + 404325503882579*T5^59 + 1659052644618213*T5^58 + 4472579947083702*T5^57 + 14315652543459822*T5^56 + 37649059309540388*T5^55 + 128864619110360619*T5^54 + 294025138592041839*T5^53 + 1033452734521007874*T5^52 + 2121865508714327788*T5^51 + 7735570481848415809*T5^50 + 14662561242348720024*T5^49 + 46077584885602053065*T5^48 + 99920415351804923060*T5^47 + 318237346655367065422*T5^46 + 710920729065009889255*T5^45 + 1979129350737147529287*T5^44 + 4570796338315800032579*T5^43 + 14387399096390346353583*T5^42 + 34627469094829804628994*T5^41 + 110451204600571473230884*T5^40 + 284402530395648933372376*T5^39 + 840702412706467257037689*T5^38 + 2026455134431941448675247*T5^37 + 5343526706840984144905925*T5^36 + 13115783334017103593723249*T5^35 + 33493779747259730430802265*T5^34 + 78722554691477193867955798*T5^33 + 175877391026166604666123610*T5^32 + 350325110825977037719027073*T5^31 + 616204953359604476753942083*T5^30 + 883252001841285453288871242*T5^29 + 957027858297937905461462889*T5^28 + 542418364917162958757003509*T5^27 - 392416427485586854896690335*T5^26 - 1516823534683153223800633091*T5^25 - 2058903987731692274499163333*T5^24 - 1666107552544635935237117327*T5^23 - 613602936089978951649611782*T5^22 + 80361074016129170643393868*T5^21 + 299929360251679496362285394*T5^20 + 437260832739402125344375649*T5^19 + 1105927552812178568736798898*T5^18 + 1710062628794698054861987612*T5^17 + 1514453459092727963785007997*T5^16 + 225628031242660653591485256*T5^15 - 818015127615742315386646414*T5^14 - 918810713920921701858619350*T5^13 - 381730029057978560955039581*T5^12 + 38299811163433342843453737*T5^11 + 140252139467714860389213627*T5^10 + 66938232715075180567568733*T5^9 - 440052685122805289074998*T5^8 - 10735197758234494245808940*T5^7 + 1713450624000385845255222*T5^6 + 8303497986295889710510943*T5^5 + 5984285293588171617836216*T5^4 + 2178802856302000870344154*T5^3 + 440628209673667783958438*T5^2 + 47202475670945712090676*T5 + 2132632758647781906961 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:

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