↑

Properties

Label 189.4.o.a
Level $189$
Weight $4$
Character orbit 189.o
Analytic conductor $11.151$
Analytic rank $0$
Dimension $44$
CM no
Inner twists $4$

Related objects

Downloads

Learn more

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [189,4,Mod(62,189)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(189, base_ring=CyclotomicField(6))
 
chi = DirichletCharacter(H, H._module([1, 3]))
 
N = Newforms(chi, 4, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("189.62");
 
S:= CuspForms(chi, 4);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 189 = 3^{3} \cdot 7 \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 189.o (of order \(6\), degree \(2\), not 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: \(11.1513609911\)
Analytic rank: \(0\)
Dimension: \(44\)
Relative dimension: \(22\) over \(\Q(\zeta_{6})\)
Twist minimal: no (minimal twist has level 63)
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.

\(\operatorname{Tr}(f)(q) = \) \( 44 q + 6 q^{2} + 78 q^{4} + 5 q^{7}+O(q^{10}) \) Copy content Toggle raw display
\(\operatorname{Tr}(f)(q) = \) \( 44 q + 6 q^{2} + 78 q^{4} + 5 q^{7} + 18 q^{11} - 204 q^{14} - 242 q^{16} - 34 q^{22} + 102 q^{23} - 352 q^{25} + 300 q^{28} - 246 q^{29} - 1068 q^{32} + 328 q^{37} - 170 q^{43} + 968 q^{46} - 79 q^{49} - 288 q^{50} - 1212 q^{56} - 538 q^{58} - 808 q^{64} - 4350 q^{65} - 590 q^{67} + 384 q^{70} + 5304 q^{74} + 2787 q^{77} - 302 q^{79} - 612 q^{85} + 13692 q^{86} + 1294 q^{88} + 210 q^{91} + 10194 q^{92} - 6336 q^{95}+O(q^{100}) \) 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   \( a_{2} \) \( a_{3} \) \( a_{4} \) \( a_{5} \) \( a_{6} \) \( a_{7} \) \( a_{8} \) \( a_{9} \) \( a_{10} \)
62.1 −4.27138 − 2.46608i 0 8.16312 + 14.1389i −7.65650 − 13.2614i 0 11.9101 − 14.1827i − 41.0664i 0 75.5262i
62.2 −4.27138 − 2.46608i 0 8.16312 + 14.1389i 7.65650 + 13.2614i 0 6.32750 − 17.4058i − 41.0664i 0 − 75.5262i
62.3 −3.92583 − 2.26658i 0 6.27474 + 10.8682i −0.0687529 − 0.119084i 0 2.53789 + 18.3455i − 20.6235i 0 0.623335i
62.4 −3.92583 − 2.26658i 0 6.27474 + 10.8682i 0.0687529 + 0.119084i 0 −17.1567 + 6.97489i − 20.6235i 0 − 0.623335i
62.5 −2.59186 − 1.49641i 0 0.478502 + 0.828790i −7.80147 − 13.5125i 0 −13.5435 − 12.6323i 21.0785i 0 46.6969i
62.6 −2.59186 − 1.49641i 0 0.478502 + 0.828790i 7.80147 + 13.5125i 0 17.7116 + 5.41283i 21.0785i 0 − 46.6969i
62.7 −1.93743 − 1.11857i 0 −1.49759 − 2.59390i −2.75758 − 4.77627i 0 13.1049 + 13.0867i 24.5978i 0 12.3382i
62.8 −1.93743 − 1.11857i 0 −1.49759 − 2.59390i 2.75758 + 4.77627i 0 −17.8859 − 4.80585i 24.5978i 0 − 12.3382i
62.9 −0.628557 − 0.362898i 0 −3.73661 − 6.47200i −5.53318 − 9.58374i 0 4.49570 − 17.9663i 11.2304i 0 8.03191i
62.10 −0.628557 − 0.362898i 0 −3.73661 − 6.47200i 5.53318 + 9.58374i 0 13.3114 − 12.8765i 11.2304i 0 − 8.03191i
62.11 0.0847887 + 0.0489528i 0 −3.99521 − 6.91990i −9.06347 − 15.6984i 0 12.7516 + 13.4312i − 1.56555i 0 − 1.77473i
62.12 0.0847887 + 0.0489528i 0 −3.99521 − 6.91990i 9.06347 + 15.6984i 0 −18.0075 − 4.32762i − 1.56555i 0 1.77473i
62.13 1.10556 + 0.638294i 0 −3.18516 − 5.51686i −1.59510 − 2.76280i 0 −13.1775 + 13.0136i − 18.3450i 0 − 4.07258i
62.14 1.10556 + 0.638294i 0 −3.18516 − 5.51686i 1.59510 + 2.76280i 0 −4.68134 + 17.9188i − 18.3450i 0 4.07258i
62.15 2.31807 + 1.33834i 0 −0.417710 − 0.723496i −0.223284 − 0.386739i 0 18.4159 − 1.96340i − 23.6495i 0 − 1.19532i
62.16 2.31807 + 1.33834i 0 −0.417710 − 0.723496i 0.223284 + 0.386739i 0 −7.50759 − 16.9303i − 23.6495i 0 1.19532i
62.17 3.28475 + 1.89645i 0 3.19307 + 5.53055i −9.97590 − 17.2788i 0 −13.5672 + 12.6068i − 6.12125i 0 − 75.6753i
62.18 3.28475 + 1.89645i 0 3.19307 + 5.53055i 9.97590 + 17.2788i 0 −4.13417 + 18.0529i − 6.12125i 0 75.6753i
62.19 3.38393 + 1.95371i 0 3.63397 + 6.29422i −5.82670 − 10.0921i 0 −2.49865 − 18.3509i − 2.86048i 0 − 45.5347i
62.20 3.38393 + 1.95371i 0 3.63397 + 6.29422i 5.82670 + 10.0921i 0 17.1417 − 7.01157i − 2.86048i 0 45.5347i
See all 44 embeddings
\(n\): e.g. 2-40 or 990-1000
Embeddings: e.g. 1-3 or 62.22
Significant digits:
Format:

Inner twists

Char Parity Ord Mult Type
1.a even 1 1 trivial
7.b odd 2 1 inner
9.d odd 6 1 inner
63.o even 6 1 inner

Twists

       By twisting character orbit
Char Parity Ord Mult Type Twist Min Dim
1.a even 1 1 trivial 189.4.o.a 44
3.b odd 2 1 63.4.o.a ✓ 44
7.b odd 2 1 inner 189.4.o.a 44
9.c even 3 1 63.4.o.a ✓ 44
9.c even 3 1 567.4.c.c 44
9.d odd 6 1 inner 189.4.o.a 44
9.d odd 6 1 567.4.c.c 44
21.c even 2 1 63.4.o.a ✓ 44
63.l odd 6 1 63.4.o.a ✓ 44
63.l odd 6 1 567.4.c.c 44
63.o even 6 1 inner 189.4.o.a 44
63.o even 6 1 567.4.c.c 44
    
        By twisted newform orbit
Twist Min Dim Char Parity Ord Mult Type
63.4.o.a ✓ 44 3.b odd 2 1
63.4.o.a ✓ 44 9.c even 3 1
63.4.o.a ✓ 44 21.c even 2 1
63.4.o.a ✓ 44 63.l odd 6 1
189.4.o.a 44 1.a even 1 1 trivial
189.4.o.a 44 7.b odd 2 1 inner
189.4.o.a 44 9.d odd 6 1 inner
189.4.o.a 44 63.o even 6 1 inner
567.4.c.c 44 9.c even 3 1
567.4.c.c 44 9.d odd 6 1
567.4.c.c 44 63.l odd 6 1
567.4.c.c 44 63.o even 6 1

Hecke kernels

This newform subspace is the entire newspace \(S_{4}^{\mathrm{new}}(189, [\chi])\).