↑

Properties

Label 143.2.u.a
Level $143$
Weight $2$
Character orbit 143.u
Analytic conductor $1.142$
Analytic rank $0$
Dimension $96$
Inner twists $4$

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] = [143,2,Mod(4,143)] 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("143.4"); S:= CuspForms(chi, 2); N := Newforms(S);
 
Copy content sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(143, base_ring=CyclotomicField(30)) chi = DirichletCharacter(H, H._module([6, 5])) N = Newforms(chi, 2, names="a")
 
Level: \( N \) \(=\) \( 143 = 11 \cdot 13 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 143.u (of order \(30\), degree \(8\), 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: \(1.14186074890\)
Analytic rank: \(0\)
Dimension: \(96\)
Relative dimension: \(12\) over \(\Q(\zeta_{30})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{30}]$

$q$-expansion

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

\(\operatorname{Tr}(f)(q) = \) \( 96 q - 9 q^{2} - 3 q^{3} - 13 q^{4} - 9 q^{6} - 9 q^{7} + 11 q^{9} + 12 q^{10} - 30 q^{11} - 52 q^{12} + 5 q^{13} - 16 q^{14} + 3 q^{15} + 7 q^{16} - 15 q^{17} + 3 q^{19} - 21 q^{20} + 23 q^{22} - 18 q^{23}+ \cdots - 6 q^{98}+O(q^{100}) \) 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   \( a_{2} \) \( a_{3} \) \( a_{4} \) \( a_{5} \) \( a_{6} \) \( a_{7} \) \( a_{8} \) \( a_{9} \) \( a_{10} \)
4.1 −1.07570 − 2.41606i 1.16844 + 1.29769i −3.34195 + 3.71162i 1.83560 + 2.52649i 1.87840 − 4.21895i −0.0557342 − 0.0501833i 7.53189 + 2.44726i −0.00514866 + 0.0489863i 4.12960 − 7.15267i
4.2 −1.02752 − 2.30785i −1.33190 − 1.47923i −2.93213 + 3.25646i −1.45488 − 2.00246i −2.04528 + 4.59377i 1.50000 + 1.35060i 5.72302 + 1.85952i −0.100564 + 0.956801i −3.12648 + 5.41522i
4.3 −0.695123 − 1.56127i −0.703955 − 0.781821i −0.616111 + 0.684260i 0.176715 + 0.243227i −0.731299 + 1.64253i −2.55781 − 2.30306i −1.75417 − 0.569964i 0.197894 − 1.88283i 0.256905 − 0.444972i
4.4 −0.499456 − 1.12180i −0.0731622 − 0.0812548i 0.329292 − 0.365715i 1.83355 + 2.52366i −0.0546100 + 0.122656i 3.66907 + 3.30365i −2.91044 − 0.945659i 0.312336 − 2.97168i 1.91526 − 3.31732i
4.5 −0.489312 − 1.09901i 2.13927 + 2.37590i 0.369857 − 0.410768i −0.216607 − 0.298134i 1.56437 − 3.51364i −0.0839050 − 0.0755484i −2.92070 − 0.948991i −0.754835 + 7.18178i −0.221665 + 0.383935i
4.6 −0.240249 − 0.539609i 0.362656 + 0.402770i 1.10480 − 1.22701i −1.61125 − 2.21769i 0.130211 − 0.292458i 1.04390 + 0.939933i −2.05107 − 0.666432i 0.282881 − 2.69143i −0.809586 + 1.40224i
4.7 −0.188590 − 0.423581i −2.16419 − 2.40357i 1.19441 − 1.32652i 0.608868 + 0.838035i −0.609963 + 1.37000i −1.29580 − 1.16674i −1.66909 − 0.542321i −0.779873 + 7.41999i 0.240149 − 0.415951i
4.8 0.230908 + 0.518628i 1.26389 + 1.40369i 1.12260 − 1.24678i 1.06863 + 1.47085i −0.436150 + 0.979610i −3.33388 − 3.00184i 1.98568 + 0.645186i −0.0593458 + 0.564638i −0.516066 + 0.893853i
4.9 0.413311 + 0.928311i −1.08942 − 1.20993i 0.647325 − 0.718928i −1.53276 − 2.10966i 0.672919 − 1.51140i 0.00489562 + 0.00440803i 2.86779 + 0.931802i 0.0365048 − 0.347320i 1.32491 − 2.29482i
4.10 0.635812 + 1.42806i −1.18771 − 1.31908i −0.296831 + 0.329664i 1.02844 + 1.41553i 1.12857 − 2.53480i 1.67014 + 1.50380i 2.31388 + 0.751826i −0.0157443 + 0.149797i −1.36756 + 2.36868i
4.11 0.859506 + 1.93048i 1.76928 + 1.96498i −1.64975 + 1.83224i −2.31074 − 3.18046i −2.27266 + 5.10447i −0.770220 − 0.693509i −0.935573 − 0.303986i −0.417223 + 3.96962i 4.15372 − 7.19446i
4.12 0.936529 + 2.10348i 0.260352 + 0.289150i −2.20927 + 2.45364i 0.574418 + 0.790618i −0.364394 + 0.818442i −0.586172 − 0.527791i −2.85054 − 0.926195i 0.297761 − 2.83300i −1.12509 + 1.94871i
36.1 −1.07570 + 2.41606i 1.16844 − 1.29769i −3.34195 − 3.71162i 1.83560 − 2.52649i 1.87840 + 4.21895i −0.0557342 + 0.0501833i 7.53189 − 2.44726i −0.00514866 − 0.0489863i 4.12960 + 7.15267i
36.2 −1.02752 + 2.30785i −1.33190 + 1.47923i −2.93213 − 3.25646i −1.45488 + 2.00246i −2.04528 − 4.59377i 1.50000 − 1.35060i 5.72302 − 1.85952i −0.100564 − 0.956801i −3.12648 − 5.41522i
36.3 −0.695123 + 1.56127i −0.703955 + 0.781821i −0.616111 − 0.684260i 0.176715 − 0.243227i −0.731299 − 1.64253i −2.55781 + 2.30306i −1.75417 + 0.569964i 0.197894 + 1.88283i 0.256905 + 0.444972i
36.4 −0.499456 + 1.12180i −0.0731622 + 0.0812548i 0.329292 + 0.365715i 1.83355 − 2.52366i −0.0546100 − 0.122656i 3.66907 − 3.30365i −2.91044 + 0.945659i 0.312336 + 2.97168i 1.91526 + 3.31732i
36.5 −0.489312 + 1.09901i 2.13927 − 2.37590i 0.369857 + 0.410768i −0.216607 + 0.298134i 1.56437 + 3.51364i −0.0839050 + 0.0755484i −2.92070 + 0.948991i −0.754835 − 7.18178i −0.221665 − 0.383935i
36.6 −0.240249 + 0.539609i 0.362656 − 0.402770i 1.10480 + 1.22701i −1.61125 + 2.21769i 0.130211 + 0.292458i 1.04390 − 0.939933i −2.05107 + 0.666432i 0.282881 + 2.69143i −0.809586 − 1.40224i
36.7 −0.188590 + 0.423581i −2.16419 + 2.40357i 1.19441 + 1.32652i 0.608868 − 0.838035i −0.609963 − 1.37000i −1.29580 + 1.16674i −1.66909 + 0.542321i −0.779873 − 7.41999i 0.240149 + 0.415951i
36.8 0.230908 − 0.518628i 1.26389 − 1.40369i 1.12260 + 1.24678i 1.06863 − 1.47085i −0.436150 − 0.979610i −3.33388 + 3.00184i 1.98568 − 0.645186i −0.0593458 − 0.564638i −0.516066 − 0.893853i
See all 96 embeddings
\(n\): e.g. 2-40 or 990-1000
Embeddings: e.g. 1-3 or 4.12
Significant digits:
Format:

Inner twists

Char Parity Ord Mult Type
1.a even 1 1 trivial
11.c even 5 1 inner
13.e even 6 1 inner
143.u even 30 1 inner

Twists

       By twisting character orbit
Char Parity Ord Mult Type Twist Min Dim
1.a even 1 1 trivial 143.2.u.a ✓ 96
11.c even 5 1 inner 143.2.u.a ✓ 96
13.e even 6 1 inner 143.2.u.a ✓ 96
143.u even 30 1 inner 143.2.u.a ✓ 96
    
        By twisted newform orbit
Twist Min Dim Char Parity Ord Mult Type
143.2.u.a ✓ 96 1.a even 1 1 trivial
143.2.u.a ✓ 96 11.c even 5 1 inner
143.2.u.a ✓ 96 13.e even 6 1 inner
143.2.u.a ✓ 96 143.u even 30 1 inner

Hecke kernels

This newform subspace is the entire newspace \(S_{2}^{\mathrm{new}}(143, [\chi])\).