Properties

Label 190.3.n.a
Level $190$
Weight $3$
Character orbit 190.n
Analytic conductor $5.177$
Analytic rank $0$
Dimension $72$
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] = [190,3,Mod(21,190)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(190, 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("190.21");
 
S:= CuspForms(chi, 3);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 190 = 2 \cdot 5 \cdot 19 \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 190.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: \(5.17712502285\)
Analytic rank: \(0\)
Dimension: \(72\)
Relative dimension: \(12\) 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.

\(\operatorname{Tr}(f)(q) = \) \( 72 q + 12 q^{3} - 24 q^{6} - 12 q^{9}+O(q^{10}) \) Copy content Toggle raw display
\(\operatorname{Tr}(f)(q) = \) \( 72 q + 12 q^{3} - 24 q^{6} - 12 q^{9} + 72 q^{12} + 180 q^{13} + 48 q^{14} + 72 q^{17} + 72 q^{19} - 36 q^{21} - 216 q^{22} - 120 q^{23} + 48 q^{24} - 48 q^{26} - 252 q^{27} - 144 q^{28} + 300 q^{29} + 216 q^{31} - 240 q^{33} + 48 q^{34} - 60 q^{35} + 24 q^{36} - 168 q^{38} - 192 q^{39} - 120 q^{41} - 144 q^{42} + 372 q^{43} + 120 q^{44} + 540 q^{47} + 96 q^{48} - 228 q^{49} - 12 q^{51} - 72 q^{52} + 312 q^{53} + 360 q^{54} + 276 q^{57} - 96 q^{58} - 696 q^{59} + 144 q^{61} - 600 q^{62} - 204 q^{63} + 288 q^{64} + 180 q^{65} - 96 q^{66} - 672 q^{67} - 72 q^{68} - 1404 q^{69} + 696 q^{71} - 192 q^{72} - 324 q^{73} + 144 q^{74} - 72 q^{76} - 72 q^{77} + 360 q^{78} + 36 q^{79} - 12 q^{81} + 192 q^{82} + 48 q^{83} - 168 q^{86} + 264 q^{87} - 168 q^{89} - 240 q^{90} - 432 q^{91} - 120 q^{92} - 720 q^{93} + 696 q^{97} + 48 q^{98} + 492 q^{99}+O(q^{100}) \) Copy content Toggle raw display

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 −1.39273 0.245576i −2.57446 + 3.06812i 1.87939 + 0.684040i 2.10122 0.764780i 4.33898 3.64084i −5.04257 8.73399i −2.44949 1.41421i −1.22270 6.93427i −3.11424 + 0.549124i
21.2 −1.39273 0.245576i −1.67774 + 1.99946i 1.87939 + 0.684040i −2.10122 + 0.764780i 2.82766 2.37269i −1.31266 2.27359i −2.44949 1.41421i 0.379829 + 2.15412i 3.11424 0.549124i
21.3 −1.39273 0.245576i 1.03536 1.23389i 1.87939 + 0.684040i −2.10122 + 0.764780i −1.74498 + 1.46421i 2.41544 + 4.18367i −2.44949 1.41421i 1.11231 + 6.30824i 3.11424 0.549124i
21.4 −1.39273 0.245576i 1.36309 1.62446i 1.87939 + 0.684040i 2.10122 0.764780i −2.29734 + 1.92769i 5.37129 + 9.30334i −2.44949 1.41421i 0.781958 + 4.43471i −3.11424 + 0.549124i
21.5 −1.39273 0.245576i 2.70607 3.22497i 1.87939 + 0.684040i −2.10122 + 0.764780i −4.56079 + 3.82696i −1.23095 2.13207i −2.44949 1.41421i −1.51477 8.59068i 3.11424 0.549124i
21.6 −1.39273 0.245576i 3.27506 3.90306i 1.87939 + 0.684040i 2.10122 0.764780i −5.51976 + 4.63163i −4.65931 8.07016i −2.44949 1.41421i −2.94505 16.7022i −3.11424 + 0.549124i
21.7 1.39273 + 0.245576i −1.59995 + 1.90675i 1.87939 + 0.684040i −2.10122 + 0.764780i −2.69655 + 2.26268i 0.787505 + 1.36400i 2.44949 + 1.41421i 0.486987 + 2.76184i −3.11424 + 0.549124i
21.8 1.39273 + 0.245576i −1.37923 + 1.64370i 1.87939 + 0.684040i 2.10122 0.764780i −2.32454 + 1.95052i 1.70226 + 2.94840i 2.44949 + 1.41421i 0.763353 + 4.32919i 3.11424 0.549124i
21.9 1.39273 + 0.245576i 0.639869 0.762566i 1.87939 + 0.684040i −2.10122 + 0.764780i 1.07843 0.904911i 4.68265 + 8.11058i 2.44949 + 1.41421i 1.39076 + 7.88739i −3.11424 + 0.549124i
21.10 1.39273 + 0.245576i 1.44897 1.72682i 1.87939 + 0.684040i 2.10122 0.764780i 2.44209 2.04915i −6.09672 10.5598i 2.44949 + 1.41421i 0.680457 + 3.85906i 3.11424 0.549124i
21.11 1.39273 + 0.245576i 2.62535 3.12877i 1.87939 + 0.684040i 2.10122 0.764780i 4.42475 3.71280i 3.48073 + 6.02881i 2.44949 + 1.41421i −1.33391 7.56496i 3.11424 0.549124i
21.12 1.39273 + 0.245576i 3.65518 4.35607i 1.87939 + 0.684040i −2.10122 + 0.764780i 6.16041 5.16920i −2.18145 3.77837i 2.44949 + 1.41421i −4.05220 22.9811i −3.11424 + 0.549124i
41.1 −0.909039 + 1.08335i −1.22181 3.35689i −0.347296 1.96962i 0.388289 2.20210i 4.74736 + 1.72790i −3.45517 5.98452i 2.44949 + 1.41421i −2.88148 + 2.41785i 2.03267 + 2.42245i
41.2 −0.909039 + 1.08335i −1.03511 2.84395i −0.347296 1.96962i −0.388289 + 2.20210i 4.02195 + 1.46387i 1.78310 + 3.08842i 2.44949 + 1.41421i −0.122188 + 0.102527i −2.03267 2.42245i
41.3 −0.909039 + 1.08335i 0.00657243 + 0.0180576i −0.347296 1.96962i −0.388289 + 2.20210i −0.0255373 0.00929482i 1.70435 + 2.95202i 2.44949 + 1.41421i 6.89412 5.78485i −2.03267 2.42245i
41.4 −0.909039 + 1.08335i 0.585942 + 1.60986i −0.347296 1.96962i 0.388289 2.20210i −2.27669 0.828647i −3.14961 5.45529i 2.44949 + 1.41421i 4.64607 3.89852i 2.03267 + 2.42245i
41.5 −0.909039 + 1.08335i 1.52962 + 4.20261i −0.347296 1.96962i 0.388289 2.20210i −5.94339 2.16322i 3.75037 + 6.49584i 2.44949 + 1.41421i −8.42777 + 7.07174i 2.03267 + 2.42245i
41.6 −0.909039 + 1.08335i 1.92230 + 5.28147i −0.347296 1.96962i −0.388289 + 2.20210i −7.46913 2.71854i −5.56528 9.63935i 2.44949 + 1.41421i −17.3043 + 14.5201i −2.03267 2.42245i
41.7 0.909039 1.08335i −1.74791 4.80234i −0.347296 1.96962i −0.388289 + 2.20210i −6.79154 2.47192i −3.09091 5.35361i −2.44949 1.41421i −13.1129 + 11.0030i 2.03267 + 2.42245i
41.8 0.909039 1.08335i −1.27347 3.49882i −0.347296 1.96962i 0.388289 2.20210i −4.94808 1.80095i −1.30839 2.26620i −2.44949 1.41421i −3.72564 + 3.12618i −2.03267 2.42245i
See all 72 embeddings
\(n\): e.g. 2-40 or 990-1000
Embeddings: e.g. 1-3 or 21.12
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 190.3.n.a 72
19.f odd 18 1 inner 190.3.n.a 72
    
        By twisted newform orbit
Twist Min Dim Char Parity Ord Mult Type
190.3.n.a 72 1.a even 1 1 trivial
190.3.n.a 72 19.f odd 18 1 inner

Hecke kernels

This newform subspace is the entire newspace \(S_{3}^{\mathrm{new}}(190, [\chi])\).