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Properties

Label 95.3.n.a
Level $95$
Weight $3$
Character orbit 95.n
Analytic conductor $2.589$
Analytic rank $0$
Dimension $84$
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] = [95,3,Mod(21,95)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(95, base_ring=CyclotomicField(18))
 
chi = DirichletCharacter(H, H._module([0, 1]))
 
N = Newforms(chi, 3, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("95.21");
 
S:= CuspForms(chi, 3);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 95 = 5 \cdot 19 \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 95.n (of order \(18\), degree \(6\), 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: \(2.58856251142\)
Analytic rank: \(0\)
Dimension: \(84\)
Relative dimension: \(14\) over \(\Q(\zeta_{18})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{18}]$

$q$-expansion

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

\(\operatorname{Tr}(f)(q) = \) \( 84 q - 12 q^{3} - 6 q^{4} + 42 q^{6} + 36 q^{9}+O(q^{10}) \) Copy content Toggle raw display
\(\operatorname{Tr}(f)(q) = \) \( 84 q - 12 q^{3} - 6 q^{4} + 42 q^{6} + 36 q^{9} - 30 q^{10} - 144 q^{12} - 54 q^{13} - 48 q^{14} - 6 q^{16} - 60 q^{17} + 12 q^{19} - 90 q^{21} + 216 q^{22} + 60 q^{23} - 24 q^{26} + 36 q^{27} + 384 q^{28} - 246 q^{29} + 120 q^{30} - 216 q^{31} - 300 q^{32} + 270 q^{33} - 252 q^{34} + 60 q^{35} - 216 q^{36} - 42 q^{38} + 168 q^{39} - 120 q^{40} + 312 q^{41} + 678 q^{42} - 378 q^{43} + 258 q^{44} + 810 q^{46} - 150 q^{47} - 1146 q^{48} - 234 q^{49} + 240 q^{51} - 174 q^{52} - 216 q^{53} - 114 q^{54} - 138 q^{57} + 96 q^{58} + 330 q^{59} - 180 q^{60} - 396 q^{61} + 720 q^{62} - 474 q^{63} + 300 q^{64} - 540 q^{65} - 1428 q^{66} + 558 q^{67} + 390 q^{68} + 270 q^{69} - 360 q^{70} - 576 q^{71} + 492 q^{72} + 330 q^{73} + 60 q^{74} - 252 q^{76} + 36 q^{77} + 780 q^{78} + 42 q^{79} + 240 q^{80} + 996 q^{81} - 642 q^{82} + 120 q^{83} + 972 q^{84} + 480 q^{85} + 930 q^{86} - 384 q^{87} + 1872 q^{88} + 780 q^{89} + 1230 q^{90} + 1008 q^{91} - 516 q^{92} + 1008 q^{93} - 852 q^{96} - 1362 q^{97} - 2064 q^{98} - 78 q^{99}+O(q^{100}) \) 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   \( a_{2} \) \( a_{3} \) \( a_{4} \) \( a_{5} \) \( a_{6} \) \( a_{7} \) \( a_{8} \) \( a_{9} \) \( a_{10} \)
21.1 −3.69403 − 0.651356i −3.05145 + 3.63657i 9.46279 + 3.44417i 2.10122 − 0.764780i 13.6408 − 11.4460i 4.79048 + 8.29735i −19.7185 − 11.3845i −2.35050 − 13.3303i −8.26009 + 1.45648i
21.2 −3.38441 − 0.596763i 0.0870285 − 0.103717i 7.33932 + 2.67130i −2.10122 + 0.764780i −0.356434 + 0.299084i −4.42153 − 7.65832i −11.3403 − 6.54735i 1.55965 + 8.84522i 7.56777 − 1.33440i
21.3 −2.90362 − 0.511987i 0.836615 − 0.997039i 4.41012 + 1.60515i 2.10122 − 0.764780i −2.93968 + 2.46669i −1.49079 − 2.58212i −1.76989 − 1.02185i 1.26867 + 7.19500i −6.49270 + 1.14484i
21.4 −1.95032 − 0.343894i −3.02467 + 3.60466i −0.0732937 − 0.0266767i −2.10122 + 0.764780i 7.13869 − 5.99007i −1.17526 − 2.03562i 6.99409 + 4.03804i −2.28213 − 12.9426i 4.36104 − 0.768970i
21.5 −1.55372 − 0.273963i −0.692577 + 0.825381i −1.41977 − 0.516753i 2.10122 − 0.764780i 1.30220 − 1.09267i 1.18892 + 2.05926i 7.52964 + 4.34724i 1.36124 + 7.71999i −3.47423 + 0.612601i
21.6 −0.870840 − 0.153553i −0.0215729 + 0.0257096i −3.02399 − 1.10064i −2.10122 + 0.764780i 0.0227343 − 0.0190764i 5.70995 + 9.88993i 5.52762 + 3.19137i 1.56264 + 8.86216i 1.94726 − 0.343354i
21.7 −0.583073 − 0.102812i 2.25668 − 2.68941i −3.42937 − 1.24819i −2.10122 + 0.764780i −1.59231 + 1.33611i −5.73459 − 9.93260i 3.92223 + 2.26450i −0.577471 − 3.27500i 1.30379 − 0.229894i
21.8 0.301616 + 0.0531830i −2.73780 + 3.26278i −3.67063 − 1.33600i 2.10122 − 0.764780i −0.999287 + 0.838502i −5.25527 − 9.10239i −2.09701 − 1.21071i −1.58737 − 9.00240i 0.674433 − 0.118921i
21.9 0.655660 + 0.115611i 2.92544 − 3.48640i −3.34225 − 1.21648i 2.10122 − 0.764780i 2.32116 − 1.94768i 1.56795 + 2.71577i −4.35705 − 2.51555i −2.03397 − 11.5352i 1.46610 − 0.258513i
21.10 1.83477 + 0.323519i −3.14169 + 3.74412i −0.497068 − 0.180918i −2.10122 + 0.764780i −6.97556 + 5.85319i 2.99897 + 5.19436i −7.30734 − 4.21889i −2.58539 − 14.6625i −4.10266 + 0.723410i
21.11 2.68346 + 0.473167i 2.07293 − 2.47042i 3.21832 + 1.17137i −2.10122 + 0.764780i 6.73156 − 5.64845i 1.66811 + 2.88925i −1.35721 − 0.783583i −0.243112 − 1.37876i −6.00041 + 1.05803i
21.12 2.83384 + 0.499682i 0.892239 − 1.06333i 4.02219 + 1.46396i 2.10122 − 0.764780i 3.05979 − 2.56747i −3.56588 − 6.17628i 0.698579 + 0.403325i 1.22826 + 6.96578i 6.33666 − 1.11732i
21.13 2.85393 + 0.503226i −1.81790 + 2.16649i 4.13293 + 1.50426i 2.10122 − 0.764780i −6.27839 + 5.26820i 4.42379 + 7.66222i 0.999298 + 0.576945i 0.173923 + 0.986365i 6.38159 − 1.12525i
21.14 3.77673 + 0.665940i −1.87413 + 2.23351i 10.0615 + 3.66207i −2.10122 + 0.764780i −8.56548 + 7.18729i −5.79131 − 10.0308i 22.2759 + 12.8610i 0.0866642 + 0.491497i −8.44503 + 1.48909i
41.1 −2.36066 + 2.81332i −0.526123 − 1.44551i −1.64749 − 9.34337i 0.388289 − 2.20210i 5.30869 + 1.93221i 5.52840 + 9.57548i 17.4531 + 10.0765i 5.08170 − 4.26405i 5.27860 + 6.29079i
41.2 −2.24133 + 2.67111i −0.196899 − 0.540977i −1.41669 − 8.03443i −0.388289 + 2.20210i 1.88632 + 0.686566i −6.30582 − 10.9220i 12.5572 + 7.24989i 6.64051 − 5.57205i −5.01176 − 5.97278i
41.3 −1.99379 + 2.37611i 1.65605 + 4.54997i −0.976091 − 5.53569i −0.388289 + 2.20210i −14.1130 − 5.13672i 5.59772 + 9.69554i 4.35459 + 2.51413i −11.0653 + 9.28487i −4.45825 − 5.31314i
41.4 −1.59643 + 1.90255i −1.90383 − 5.23073i −0.376515 − 2.13533i −0.388289 + 2.20210i 12.9910 + 4.72835i 1.82126 + 3.15451i −3.93980 − 2.27465i −16.8416 + 14.1318i −3.56972 − 4.25423i
41.5 −1.16381 + 1.38697i −0.993536 − 2.72972i 0.125350 + 0.710895i 0.388289 − 2.20210i 4.94233 + 1.79886i −1.94260 − 3.36468i −7.40385 − 4.27461i 0.430149 − 0.360938i 2.60235 + 3.10136i
41.6 −0.717745 + 0.855375i 0.875927 + 2.40659i 0.478084 + 2.71135i −0.388289 + 2.20210i −2.68723 − 0.978071i −1.20177 − 2.08152i −6.53042 − 3.77034i 1.86997 − 1.56909i −1.60493 − 1.91268i
See all 84 embeddings
\(n\): e.g. 2-40 or 990-1000
Embeddings: e.g. 1-3 or 21.14
Significant digits:
Format:

Inner twists

Char Parity Ord Mult Type
1.a even 1 1 trivial
19.f odd 18 1 inner

Twists

       By twisting character orbit
Char Parity Ord Mult Type Twist Min Dim
1.a even 1 1 trivial 95.3.n.a ✓ 84
19.f odd 18 1 inner 95.3.n.a ✓ 84
    
        By twisted newform orbit
Twist Min Dim Char Parity Ord Mult Type
95.3.n.a ✓ 84 1.a even 1 1 trivial
95.3.n.a ✓ 84 19.f odd 18 1 inner

Hecke kernels

This newform subspace is the entire newspace \(S_{3}^{\mathrm{new}}(95, [\chi])\).