↑

Properties

Label 143.3.m.a
Level $143$
Weight $3$
Character orbit 143.m
Analytic conductor $3.896$
Analytic rank $0$
Dimension $96$
Inner twists $2$

Related objects

Downloads

Learn more

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

Copy content comment:Compute space of new eigenforms
 
Copy content gp:[N,k,chi] = [143,3,Mod(40,143)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)
 
Copy content magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("143.40"); S:= CuspForms(chi, 3); N := Newforms(S);
 
Copy content sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(143, base_ring=CyclotomicField(10)) chi = DirichletCharacter(H, H._module([7, 0])) N = Newforms(chi, 3, names="a")
 
Level: \( N \) \(=\) \( 143 = 11 \cdot 13 \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 143.m (of order \(10\), degree \(4\), minimal)

Newform invariants

Copy content comment:select newform
 
Copy content sage:traces = [] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(0)] == traces)
 
Copy content gp:f = lf[1] \\ Warning: the index may be different
 
Self dual: no
Analytic conductor: \(3.89646778035\)
Analytic rank: \(0\)
Dimension: \(96\)
Relative dimension: \(24\) over \(\Q(\zeta_{10})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{10}]$

$q$-expansion

The algebraic \(q\)-expansion of this newform has not been computed, but we have computed the trace expansion.

\(\operatorname{Tr}(f)(q) = \) \( 96 q - 6 q^{3} + 60 q^{4} + 2 q^{5} - 40 q^{6} - 30 q^{7} - 40 q^{8} - 38 q^{9} - 14 q^{11} + 88 q^{12} - 50 q^{14} - 54 q^{15} - 104 q^{16} + 30 q^{17} - 70 q^{18} - 60 q^{19} - 16 q^{20} - 4 q^{22} + 20 q^{23}+ \cdots + 1064 q^{99}+O(q^{100}) \) 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.

Copy content comment:embeddings in the coefficient field
 
Copy content gp:mfembed(f)
 
Label   \( a_{2} \) \( a_{3} \) \( a_{4} \) \( a_{5} \) \( a_{6} \) \( a_{7} \) \( a_{8} \) \( a_{9} \) \( a_{10} \)
40.1 −2.25017 + 3.09710i −0.174658 + 0.537542i −3.29266 − 10.1338i 5.96502 − 4.33384i −1.27181 − 1.75049i −8.49604 + 2.76053i 24.2309 + 7.87310i 7.02271 + 5.10230i 28.2261i
40.2 −2.05258 + 2.82514i −0.606873 + 1.86776i −2.53225 − 7.79346i −6.73745 + 4.89505i −4.03103 − 5.54824i −1.29391 + 0.420416i 13.9307 + 4.52634i 4.16091 + 3.02308i − 29.0818i
40.3 −1.82290 + 2.50901i −0.459035 + 1.41276i −1.73608 − 5.34312i 3.51750 − 2.55561i −2.70786 − 3.72705i 13.1031 − 4.25746i 4.77256 + 1.55070i 5.49596 + 3.99305i 13.4841i
40.4 −1.75062 + 2.40953i −1.79671 + 5.52970i −1.50507 − 4.63213i 0.237936 − 0.172871i −10.1786 − 14.0097i −0.322468 + 0.104776i 2.46577 + 0.801179i −20.0683 − 14.5805i 0.875944i
40.5 −1.48599 + 2.04529i 1.52814 − 4.70314i −0.738985 − 2.27436i 5.65599 − 4.10932i 7.34850 + 10.1143i −2.92829 + 0.951459i −3.86768 − 1.25669i −12.5032 − 9.08409i 17.6746i
40.6 −1.24282 + 1.71060i −0.191245 + 0.588591i −0.145468 − 0.447704i 0.856348 − 0.622173i −0.769159 − 1.05866i −7.33280 + 2.38257i −7.09708 − 2.30598i 6.97129 + 5.06494i 2.23812i
40.7 −1.01215 + 1.39310i 0.524851 − 1.61533i 0.319782 + 0.984187i −1.02892 + 0.747553i 1.71908 + 2.36611i 9.44691 − 3.06949i −8.24548 − 2.67912i 4.94735 + 3.59446i − 2.19002i
40.8 −0.692275 + 0.952835i −0.999026 + 3.07469i 0.807418 + 2.48498i −2.63678 + 1.91573i −2.23807 − 3.08044i −3.29627 + 1.07102i −7.40723 − 2.40675i −1.17449 − 0.853320i − 3.83863i
40.9 −0.459224 + 0.632068i 1.24726 − 3.83867i 1.04745 + 3.22370i −7.15021 + 5.19493i 1.85353 + 2.55116i −6.46840 + 2.10171i −5.49077 − 1.78406i −5.89855 − 4.28555i − 6.90505i
40.10 −0.354398 + 0.487787i 0.286945 − 0.883126i 1.12373 + 3.45848i 4.79996 − 3.48738i 0.329085 + 0.452946i −2.58976 + 0.841466i −4.37896 − 1.42281i 6.58358 + 4.78325i 3.57728i
40.11 −0.0858052 + 0.118101i −1.33575 + 4.11101i 1.22948 + 3.78396i −4.65764 + 3.38397i −0.370899 − 0.510498i 10.6872 − 3.47247i −1.10773 − 0.359922i −7.83500 − 5.69246i − 0.840433i
40.12 −0.0784398 + 0.107963i −1.18685 + 3.65275i 1.23056 + 3.78729i 7.67079 − 5.57316i −0.301266 − 0.414657i 5.40142 − 1.75503i −1.01309 − 0.329172i −4.65283 − 3.38048i 1.26532i
40.13 0.154453 − 0.212586i 1.74576 − 5.37289i 1.21473 + 3.73856i 1.15845 − 0.841664i −0.872566 − 1.20098i 8.40798 − 2.73192i 1.98203 + 0.644000i −18.5391 − 13.4694i − 0.376269i
40.14 0.574893 − 0.791272i 0.797782 − 2.45532i 0.940458 + 2.89443i 2.79666 − 2.03189i −1.48419 − 2.04281i 1.75809 − 0.571238i 6.55173 + 2.12879i 1.88902 + 1.37245i − 3.38104i
40.15 0.692275 − 0.952835i −0.103531 + 0.318637i 0.807418 + 2.48498i −3.71025 + 2.69566i 0.231936 + 0.319233i −7.78245 + 2.52867i 7.40723 + 2.40675i 7.19034 + 5.22409i 5.40139i
40.16 0.747289 − 1.02856i −1.47493 + 4.53937i 0.736583 + 2.26697i 1.86103 − 1.35211i 3.56680 + 4.90927i −11.8373 + 3.84617i 7.71870 + 2.50796i −11.1493 − 8.10047i − 2.92459i
40.17 0.803724 − 1.10623i 0.117878 − 0.362791i 0.658293 + 2.02602i −5.23359 + 3.80243i −0.306589 − 0.421984i 5.79097 − 1.88160i 7.97214 + 2.59031i 7.16343 + 5.20454i 8.84567i
40.18 1.51740 − 2.08852i 0.867180 − 2.66890i −0.823358 − 2.53403i 6.07267 − 4.41205i −4.25821 − 5.86093i −8.32542 + 2.70509i 3.27907 + 1.06544i 0.910102 + 0.661228i − 19.3778i
40.19 1.54611 − 2.12804i −0.707131 + 2.17633i −0.902026 − 2.77615i 1.31307 − 0.954003i 3.53800 + 4.86965i 7.07964 − 2.30031i 2.70425 + 0.878665i 3.04479 + 2.21217i − 4.26927i
40.20 1.54746 − 2.12989i −1.05303 + 3.24091i −0.905745 − 2.78760i 2.91232 − 2.11593i 5.27325 + 7.25801i 1.61725 − 0.525477i 2.67647 + 0.869637i −2.11344 − 1.53550i − 9.47723i
See all 96 embeddings
\(n\): e.g. 2-40 or 990-1000
Embeddings: e.g. 1-3 or 40.24
Significant digits:
Format:

Inner twists

Char Parity Ord Mult Type
1.a even 1 1 trivial
11.d odd 10 1 inner

Twists

       By twisting character orbit
Char Parity Ord Mult Type Twist Min Dim
1.a even 1 1 trivial 143.3.m.a ✓ 96
11.d odd 10 1 inner 143.3.m.a ✓ 96
    
        By twisted newform orbit
Twist Min Dim Char Parity Ord Mult Type
143.3.m.a ✓ 96 1.a even 1 1 trivial
143.3.m.a ✓ 96 11.d odd 10 1 inner

Hecke kernels

This newform subspace is the entire newspace \(S_{3}^{\mathrm{new}}(143, [\chi])\).