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Properties

Label 855.2.i.d
Level $855$
Weight $2$
Character orbit 855.i
Analytic conductor $6.827$
Analytic rank $0$
Dimension $46$
CM no
Inner twists $2$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [855,2,Mod(286,855)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(855, base_ring=CyclotomicField(6))
 
chi = DirichletCharacter(H, H._module([4, 0, 0]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("855.286");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 855 = 3^{2} \cdot 5 \cdot 19 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 855.i (of order \(3\), degree \(2\), 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: \(6.82720937282\)
Analytic rank: \(0\)
Dimension: \(46\)
Relative dimension: \(23\) over \(\Q(\zeta_{3})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

$q$-expansion

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

\(\operatorname{Tr}(f)(q) = \) \( 46 q + 3 q^{2} + 2 q^{3} - 29 q^{4} + 23 q^{5} + 3 q^{6} - 10 q^{7} - 12 q^{8} - 8 q^{9}+O(q^{10}) \) Copy content Toggle raw display
\(\operatorname{Tr}(f)(q) = \) \( 46 q + 3 q^{2} + 2 q^{3} - 29 q^{4} + 23 q^{5} + 3 q^{6} - 10 q^{7} - 12 q^{8} - 8 q^{9} + 6 q^{10} - q^{11} + 9 q^{12} - 11 q^{13} - 3 q^{14} + q^{15} - 45 q^{16} - 30 q^{17} - 18 q^{18} + 46 q^{19} + 29 q^{20} - 2 q^{21} - 5 q^{22} + 13 q^{23} - 6 q^{24} - 23 q^{25} - 12 q^{26} + 23 q^{27} + 56 q^{28} + 2 q^{29} + 6 q^{30} - 16 q^{31} + 25 q^{32} + 19 q^{33} - 18 q^{34} - 20 q^{35} - 5 q^{36} + 58 q^{37} + 3 q^{38} + 32 q^{39} - 6 q^{40} + 14 q^{41} - 67 q^{42} - 34 q^{43} + 64 q^{44} - 7 q^{45} - 4 q^{46} + 22 q^{47} + 89 q^{48} - 61 q^{49} + 3 q^{50} - 38 q^{51} - 20 q^{52} - 70 q^{53} - 91 q^{54} - 2 q^{55} - 26 q^{56} + 2 q^{57} - 23 q^{58} - 15 q^{59} + 3 q^{60} - 32 q^{61} + 6 q^{62} - 31 q^{63} + 164 q^{64} + 11 q^{65} + 54 q^{66} - 16 q^{67} + 26 q^{68} - 19 q^{69} + 3 q^{70} + 50 q^{71} + 22 q^{72} + 82 q^{73} + 9 q^{74} - q^{75} - 29 q^{76} + 18 q^{77} - 41 q^{78} - 11 q^{79} - 90 q^{80} + 8 q^{81} + 60 q^{82} + 26 q^{83} + 123 q^{84} - 15 q^{85} - 15 q^{86} - 26 q^{87} - 22 q^{88} + 40 q^{89} - 12 q^{90} + 116 q^{91} + 2 q^{92} + 42 q^{93} - 36 q^{94} + 23 q^{95} - 48 q^{96} - 50 q^{97} - 24 q^{98} - 29 q^{99}+O(q^{100}) \) Copy content Toggle raw display

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   \( a_{2} \) \( a_{3} \) \( a_{4} \) \( a_{5} \) \( a_{6} \) \( a_{7} \) \( a_{8} \) \( a_{9} \) \( a_{10} \)
286.1 −1.37295 + 2.37803i −0.953334 − 1.44608i −2.77000 − 4.79779i 0.500000 + 0.866025i 4.74771 − 0.281649i −0.580361 + 1.00522i 9.72054 −1.18231 + 2.75720i −2.74591
286.2 −1.28784 + 2.23061i 1.73147 − 0.0447269i −2.31709 − 4.01331i 0.500000 + 0.866025i −2.13010 + 3.91985i −2.35587 + 4.08049i 6.78480 2.99600 − 0.154887i −2.57569
286.3 −1.20815 + 2.09257i −1.65368 + 0.515118i −1.91923 − 3.32421i 0.500000 + 0.866025i 0.919966 − 4.08278i 0.0196889 − 0.0341022i 4.44227 2.46931 − 1.70368i −2.41629
286.4 −1.04031 + 1.80187i −0.431939 + 1.67733i −1.16450 − 2.01698i 0.500000 + 0.866025i −2.57298 − 2.52325i 1.56804 − 2.71593i 0.684535 −2.62686 − 1.44901i −2.08063
286.5 −0.876140 + 1.51752i 0.239525 − 1.71541i −0.535244 − 0.927070i 0.500000 + 0.866025i 2.39331 + 1.86642i −0.602689 + 1.04389i −1.62877 −2.88526 − 0.821768i −1.75228
286.6 −0.827277 + 1.43289i 1.37593 + 1.05205i −0.368776 − 0.638738i 0.500000 + 0.866025i −2.64575 + 1.10121i 2.45202 − 4.24703i −2.08879 0.786362 + 2.89511i −1.65455
286.7 −0.756464 + 1.31023i −0.843056 + 1.51303i −0.144476 − 0.250240i 0.500000 + 0.866025i −1.34468 − 2.24915i −2.43933 + 4.22504i −2.58869 −1.57851 − 2.55114i −1.51293
286.8 −0.531693 + 0.920920i 1.65145 + 0.522212i 0.434605 + 0.752757i 0.500000 + 0.866025i −1.35898 + 1.24320i −0.701211 + 1.21453i −3.05108 2.45459 + 1.72482i −1.06339
286.9 −0.312675 + 0.541569i −1.37123 − 1.05817i 0.804468 + 1.39338i 0.500000 + 0.866025i 1.00182 − 0.411750i −0.216265 + 0.374582i −2.25685 0.760533 + 2.90200i −0.625351
286.10 −0.105950 + 0.183511i −1.71778 − 0.221918i 0.977549 + 1.69316i 0.500000 + 0.866025i 0.222723 − 0.291719i −1.66066 + 2.87634i −0.838087 2.90150 + 0.762411i −0.211900
286.11 0.0156585 − 0.0271212i −0.176375 − 1.72305i 0.999510 + 1.73120i 0.500000 + 0.866025i −0.0494929 − 0.0221967i 1.08606 − 1.88111i 0.125237 −2.93778 + 0.607806i 0.0313169
286.12 0.0851852 − 0.147545i 1.08936 − 1.34659i 0.985487 + 1.70691i 0.500000 + 0.866025i −0.105886 − 0.275439i 1.49254 − 2.58516i 0.676537 −0.626611 − 2.93383i 0.170370
286.13 0.0983098 − 0.170278i 0.994216 + 1.41829i 0.980670 + 1.69857i 0.500000 + 0.866025i 0.339244 − 0.0298612i 0.566167 − 0.980630i 0.778878 −1.02307 + 2.82016i 0.196620
286.14 0.537852 − 0.931586i 0.841993 + 1.51362i 0.421431 + 0.729940i 0.500000 + 0.866025i 1.86294 + 0.0297148i −2.18450 + 3.78366i 3.05808 −1.58210 + 2.54892i 1.07570
286.15 0.566413 − 0.981056i −0.301099 − 1.70568i 0.358352 + 0.620685i 0.500000 + 0.866025i −1.84391 − 0.670723i −2.11018 + 3.65494i 3.07755 −2.81868 + 1.02716i 1.13283
286.16 0.623036 − 1.07913i −0.787472 + 1.54269i 0.223652 + 0.387377i 0.500000 + 0.866025i 1.17414 + 1.81094i 1.90221 − 3.29472i 3.04952 −1.75978 − 2.42965i 1.24607
286.17 0.744981 − 1.29034i 1.23726 − 1.21210i −0.109993 − 0.190514i 0.500000 + 0.866025i −0.642296 − 2.49948i −1.40618 + 2.43557i 2.65215 0.0616154 − 2.99937i 1.48996
286.18 0.949697 − 1.64492i 1.57344 − 0.724068i −0.803848 − 1.39231i 0.500000 + 0.866025i 0.303258 − 3.27584i 2.16725 − 3.75380i 0.745138 1.95145 − 2.27856i 1.89939
286.19 1.06408 − 1.84303i −1.72953 − 0.0934107i −1.26451 − 2.19020i 0.500000 + 0.866025i −2.01251 + 3.08818i −0.718210 + 1.24398i −1.12585 2.98255 + 0.323113i 2.12815
286.20 1.09397 − 1.89482i −0.912613 + 1.47212i −1.39356 − 2.41372i 0.500000 + 0.866025i 1.79103 + 3.33970i 0.0813308 − 0.140869i −1.72218 −1.33427 − 2.68695i 2.18795
See all 46 embeddings
\(n\): e.g. 2-40 or 990-1000
Embeddings: e.g. 1-3 or 286.23
Significant digits:
Format:

Inner twists

Char Parity Ord Mult Type
1.a even 1 1 trivial
9.c even 3 1 inner

Twists

       By twisting character orbit
Char Parity Ord Mult Type Twist Min Dim
1.a even 1 1 trivial 855.2.i.d ✓ 46
9.c even 3 1 inner 855.2.i.d ✓ 46
9.c even 3 1 7695.2.a.w 23
9.d odd 6 1 7695.2.a.x 23
    
        By twisted newform orbit
Twist Min Dim Char Parity Ord Mult Type
855.2.i.d ✓ 46 1.a even 1 1 trivial
855.2.i.d ✓ 46 9.c even 3 1 inner
7695.2.a.w 23 9.c even 3 1
7695.2.a.x 23 9.d odd 6 1

Hecke kernels

This newform subspace can be constructed as the kernel of the linear operator \( T_{2}^{46} - 3 T_{2}^{45} + 42 T_{2}^{44} - 105 T_{2}^{43} + 940 T_{2}^{42} - 2105 T_{2}^{41} + \cdots + 81 \) acting on \(S_{2}^{\mathrm{new}}(855, [\chi])\). Copy content Toggle raw display