↑

Properties

Label 190.3.j.a
Level $190$
Weight $3$
Character orbit 190.j
Analytic conductor $5.177$
Analytic rank $0$
Dimension $32$
CM no
Inner twists $2$

Related objects

Downloads

Learn more

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [190,3,Mod(31,190)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(190, base_ring=CyclotomicField(6))
 
chi = DirichletCharacter(H, H._module([0, 5]))
 
N = Newforms(chi, 3, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("190.31");
 
S:= CuspForms(chi, 3);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 190 = 2 \cdot 5 \cdot 19 \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 190.j (of order \(6\), 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: \(5.17712502285\)
Analytic rank: \(0\)
Dimension: \(32\)
Relative dimension: \(16\) over \(\Q(\zeta_{6})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{6}]$

$q$-expansion

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

\(\operatorname{Tr}(f)(q) = \) \( 32 q - 12 q^{3} + 32 q^{4} + 8 q^{6} + 8 q^{7} + 76 q^{9}+O(q^{10}) \) Copy content Toggle raw display
\(\operatorname{Tr}(f)(q) = \) \( 32 q - 12 q^{3} + 32 q^{4} + 8 q^{6} + 8 q^{7} + 76 q^{9} + 32 q^{11} + 60 q^{13} + 24 q^{14} - 64 q^{16} - 36 q^{17} - 68 q^{19} - 4 q^{23} - 16 q^{24} - 80 q^{25} - 32 q^{26} + 8 q^{28} - 12 q^{29} + 240 q^{33} - 48 q^{34} + 20 q^{35} - 152 q^{36} + 64 q^{38} + 200 q^{39} - 24 q^{41} + 48 q^{43} + 32 q^{44} - 80 q^{45} - 48 q^{47} + 48 q^{48} + 48 q^{49} - 240 q^{51} + 120 q^{52} + 120 q^{53} + 32 q^{54} - 152 q^{57} - 288 q^{58} + 156 q^{59} - 24 q^{61} + 64 q^{62} - 156 q^{63} - 256 q^{64} - 80 q^{66} - 252 q^{67} - 144 q^{68} - 552 q^{71} - 96 q^{72} + 260 q^{73} + 40 q^{76} + 200 q^{77} - 360 q^{78} - 84 q^{79} - 240 q^{81} + 240 q^{82} - 776 q^{83} + 456 q^{86} + 360 q^{87} - 84 q^{89} + 240 q^{90} - 120 q^{91} + 8 q^{92} + 568 q^{93} - 120 q^{95} - 64 q^{96} + 456 q^{97} - 48 q^{98} - 416 q^{99}+O(q^{100}) \) 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   \( a_{2} \) \( a_{3} \) \( a_{4} \) \( a_{5} \) \( a_{6} \) \( a_{7} \) \( a_{8} \) \( a_{9} \) \( a_{10} \)
31.1 −1.22474 + 0.707107i −5.10798 + 2.94910i 1.00000 − 1.73205i −1.11803 − 1.93649i 4.17065 − 7.22378i −8.17129 2.82843i 12.8943 − 22.3336i 2.73861 + 1.58114i
31.2 −1.22474 + 0.707107i −3.65136 + 2.10811i 1.00000 − 1.73205i 1.11803 + 1.93649i 2.98132 − 5.16380i 13.1700 2.82843i 4.38828 − 7.60073i −2.73861 − 1.58114i
31.3 −1.22474 + 0.707107i −2.46057 + 1.42061i 1.00000 − 1.73205i 1.11803 + 1.93649i 2.00904 − 3.47977i −5.98551 2.82843i −0.463743 + 0.803226i −2.73861 − 1.58114i
31.4 −1.22474 + 0.707107i −1.43677 + 0.829522i 1.00000 − 1.73205i −1.11803 − 1.93649i 1.17312 − 2.03190i 5.23225 2.82843i −3.12379 + 5.41056i 2.73861 + 1.58114i
31.5 −1.22474 + 0.707107i −0.706638 + 0.407978i 1.00000 − 1.73205i −1.11803 − 1.93649i 0.576967 − 0.999337i −0.856692 2.82843i −4.16711 + 7.21764i 2.73861 + 1.58114i
31.6 −1.22474 + 0.707107i 1.02932 − 0.594276i 1.00000 − 1.73205i 1.11803 + 1.93649i −0.840433 + 1.45567i −9.87592 2.82843i −3.79367 + 6.57083i −2.73861 − 1.58114i
31.7 −1.22474 + 0.707107i 2.35786 − 1.36131i 1.00000 − 1.73205i 1.11803 + 1.93649i −1.92519 + 3.33452i 3.47803 2.82843i −0.793650 + 1.37464i −2.73861 − 1.58114i
31.8 −1.22474 + 0.707107i 4.52665 − 2.61346i 1.00000 − 1.73205i −1.11803 − 1.93649i −3.69599 + 6.40165i 0.110169 2.82843i 9.16037 − 15.8662i 2.73861 + 1.58114i
31.9 1.22474 − 0.707107i −4.86674 + 2.80981i 1.00000 − 1.73205i 1.11803 + 1.93649i −3.97368 + 6.88261i −1.21390 − 2.82843i 11.2901 − 19.5551i 2.73861 + 1.58114i
31.10 1.22474 − 0.707107i −3.89886 + 2.25101i 1.00000 − 1.73205i −1.11803 − 1.93649i −3.18341 + 5.51382i 5.93147 − 2.82843i 5.63407 − 9.75849i −2.73861 − 1.58114i
31.11 1.22474 − 0.707107i −2.19594 + 1.26783i 1.00000 − 1.73205i −1.11803 − 1.93649i −1.79298 + 3.10553i −9.66125 − 2.82843i −1.28522 + 2.22607i −2.73861 − 1.58114i
31.12 1.22474 − 0.707107i −2.00431 + 1.15719i 1.00000 − 1.73205i 1.11803 + 1.93649i −1.63651 + 2.83452i 2.74988 − 2.82843i −1.82182 + 3.15549i 2.73861 + 1.58114i
31.13 1.22474 − 0.707107i 1.66365 − 0.960506i 1.00000 − 1.73205i −1.11803 − 1.93649i 1.35836 − 2.35275i 10.8839 − 2.82843i −2.65485 + 4.59834i −2.73861 − 1.58114i
31.14 1.22474 − 0.707107i 2.89093 − 1.66908i 1.00000 − 1.73205i 1.11803 + 1.93649i 2.36043 − 4.08839i 8.94073 − 2.82843i 1.07164 − 1.85614i 2.73861 + 1.58114i
31.15 1.22474 − 0.707107i 3.70487 − 2.13901i 1.00000 − 1.73205i 1.11803 + 1.93649i 3.02501 − 5.23948i −4.79116 − 2.82843i 4.65071 − 8.05527i 2.73861 + 1.58114i
31.16 1.22474 − 0.707107i 4.15590 − 2.39941i 1.00000 − 1.73205i −1.11803 − 1.93649i 3.39328 − 5.87733i −5.94074 − 2.82843i 7.01434 − 12.1492i −2.73861 − 1.58114i
141.1 −1.22474 − 0.707107i −5.10798 − 2.94910i 1.00000 + 1.73205i −1.11803 + 1.93649i 4.17065 + 7.22378i −8.17129 − 2.82843i 12.8943 + 22.3336i 2.73861 − 1.58114i
141.2 −1.22474 − 0.707107i −3.65136 − 2.10811i 1.00000 + 1.73205i 1.11803 − 1.93649i 2.98132 + 5.16380i 13.1700 − 2.82843i 4.38828 + 7.60073i −2.73861 + 1.58114i
141.3 −1.22474 − 0.707107i −2.46057 − 1.42061i 1.00000 + 1.73205i 1.11803 − 1.93649i 2.00904 + 3.47977i −5.98551 − 2.82843i −0.463743 − 0.803226i −2.73861 + 1.58114i
141.4 −1.22474 − 0.707107i −1.43677 − 0.829522i 1.00000 + 1.73205i −1.11803 + 1.93649i 1.17312 + 2.03190i 5.23225 − 2.82843i −3.12379 − 5.41056i 2.73861 − 1.58114i
See all 32 embeddings
\(n\): e.g. 2-40 or 990-1000
Embeddings: e.g. 1-3 or 31.16
Significant digits:
Format:

Inner twists

Char Parity Ord Mult Type
1.a even 1 1 trivial
19.d odd 6 1 inner

Twists

       By twisting character orbit
Char Parity Ord Mult Type Twist Min Dim
1.a even 1 1 trivial 190.3.j.a ✓ 32
19.d odd 6 1 inner 190.3.j.a ✓ 32
    
        By twisted newform orbit
Twist Min Dim Char Parity Ord Mult Type
190.3.j.a ✓ 32 1.a even 1 1 trivial
190.3.j.a ✓ 32 19.d odd 6 1 inner

Hecke kernels

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