Properties

Label 143.3.f.a
Level $143$
Weight $3$
Character orbit 143.f
Analytic conductor $3.896$
Analytic rank $0$
Dimension $44$
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] = [143,3,Mod(34,143)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(143, base_ring=CyclotomicField(4))
 
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("143.34");
 
S:= CuspForms(chi, 3);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 143 = 11 \cdot 13 \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 143.f (of order \(4\), 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: \(3.89646778035\)
Analytic rank: \(0\)
Dimension: \(44\)
Relative dimension: \(22\) over \(\Q(i)\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{4}]$

$q$-expansion

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

\(\operatorname{Tr}(f)(q) = \) \( 44 q + 4 q^{2} - 20 q^{5} + 12 q^{6} + 20 q^{7} - 60 q^{8} + 108 q^{9}+O(q^{10}) \) Copy content Toggle raw display
\(\operatorname{Tr}(f)(q) = \) \( 44 q + 4 q^{2} - 20 q^{5} + 12 q^{6} + 20 q^{7} - 60 q^{8} + 108 q^{9} - 40 q^{13} - 16 q^{14} + 32 q^{15} - 80 q^{16} - 88 q^{18} + 4 q^{19} + 64 q^{20} - 96 q^{21} - 48 q^{24} + 92 q^{26} + 48 q^{27} + 156 q^{28} + 120 q^{29} - 112 q^{31} - 156 q^{32} + 112 q^{34} + 88 q^{35} - 120 q^{37} - 96 q^{39} + 64 q^{40} - 12 q^{41} + 100 q^{42} + 88 q^{44} - 200 q^{45} - 316 q^{46} - 164 q^{47} + 340 q^{48} + 148 q^{50} - 280 q^{52} - 256 q^{53} + 88 q^{54} - 92 q^{57} + 60 q^{58} - 360 q^{59} + 460 q^{60} + 552 q^{61} - 264 q^{63} + 492 q^{65} - 220 q^{66} - 232 q^{67} - 576 q^{68} + 348 q^{70} - 16 q^{71} + 92 q^{72} - 76 q^{73} - 144 q^{74} - 64 q^{76} - 88 q^{78} + 152 q^{79} - 24 q^{80} + 236 q^{81} + 220 q^{83} + 364 q^{84} + 512 q^{85} - 352 q^{86} - 816 q^{87} + 196 q^{89} + 104 q^{91} + 1180 q^{92} - 180 q^{93} - 704 q^{94} - 1068 q^{96} + 392 q^{97} - 144 q^{98}+O(q^{100}) \) 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.

comment: embeddings in the coefficient field
 
gp: mfembed(f)
 
Label   \( a_{2} \) \( a_{3} \) \( a_{4} \) \( a_{5} \) \( a_{6} \) \( a_{7} \) \( a_{8} \) \( a_{9} \) \( a_{10} \)
34.1 −2.64015 2.64015i −4.33590 9.94077i 1.25926 + 1.25926i 11.4474 + 11.4474i −0.913684 + 0.913684i 15.6845 15.6845i 9.80004 6.64925i
34.2 −2.22621 2.22621i −0.558224 5.91203i −6.02578 6.02578i 1.24272 + 1.24272i 9.68125 9.68125i 4.25659 4.25659i −8.68839 26.8293i
34.3 −1.85438 1.85438i 5.20150 2.87745i 2.96117 + 2.96117i −9.64555 9.64555i 2.87608 2.87608i −2.08163 + 2.08163i 18.0556 10.9823i
34.4 −1.73011 1.73011i 0.410741 1.98654i 4.09492 + 4.09492i −0.710625 0.710625i −5.63695 + 5.63695i −3.48350 + 3.48350i −8.83129 14.1693i
34.5 −1.68515 1.68515i 3.72208 1.67948i −6.45193 6.45193i −6.27228 6.27228i −5.94039 + 5.94039i −3.91043 + 3.91043i 4.85388 21.7450i
34.6 −1.59151 1.59151i −2.93230 1.06581i −1.63050 1.63050i 4.66679 + 4.66679i −2.09617 + 2.09617i −4.66980 + 4.66980i −0.401600 5.18992i
34.7 −1.51765 1.51765i −4.16131 0.606507i 5.29838 + 5.29838i 6.31540 + 6.31540i 6.10478 6.10478i −5.15013 + 5.15013i 8.31650 16.0822i
34.8 −0.776817 0.776817i 3.30077 2.79311i −0.0738022 0.0738022i −2.56409 2.56409i 6.38010 6.38010i −5.27701 + 5.27701i 1.89508 0.114662i
34.9 −0.559583 0.559583i −0.674236 3.37373i −0.687945 0.687945i 0.377291 + 0.377291i 2.77474 2.77474i −4.12622 + 4.12622i −8.54541 0.769925i
34.10 −0.552131 0.552131i −5.92566 3.39030i −4.73402 4.73402i 3.27174 + 3.27174i −0.106091 + 0.106091i −4.08041 + 4.08041i 26.1135 5.22760i
34.11 −0.0486638 0.0486638i −0.462719 3.99526i −2.85396 2.85396i 0.0225177 + 0.0225177i −7.80024 + 7.80024i −0.389080 + 0.389080i −8.78589 0.277769i
34.12 0.155288 + 0.155288i 1.56388 3.95177i 6.66238 + 6.66238i 0.242851 + 0.242851i 0.683897 0.683897i 1.23481 1.23481i −6.55429 2.06918i
34.13 0.356298 + 0.356298i 5.60622 3.74610i 1.97185 + 1.97185i 1.99748 + 1.99748i −7.27233 + 7.27233i 2.75992 2.75992i 22.4297 1.40513i
34.14 0.691450 + 0.691450i 3.83291 3.04379i −4.28548 4.28548i 2.65027 + 2.65027i 1.74284 1.74284i 4.87043 4.87043i 5.69120 5.92639i
34.15 1.26289 + 1.26289i −1.31481 0.810231i −4.90134 4.90134i −1.66046 1.66046i 3.17698 3.17698i 6.07478 6.07478i −7.27126 12.3797i
34.16 1.32847 + 1.32847i −4.01579 0.470326i 0.202377 + 0.202377i −5.33487 5.33487i 7.08212 7.08212i 5.93870 5.93870i 7.12659 0.537703i
34.17 1.53765 + 1.53765i 1.81506 0.728748i 3.39071 + 3.39071i 2.79093 + 2.79093i 4.13599 4.13599i 5.03005 5.03005i −5.70557 10.4275i
34.18 2.04521 + 2.04521i 2.72146 4.36577i 0.836799 + 0.836799i 5.56597 + 5.56597i −4.60563 + 4.60563i −0.748085 + 0.748085i −1.59364 3.42286i
34.19 2.20615 + 2.20615i −2.86898 5.73423i 3.26224 + 3.26224i −6.32941 6.32941i −5.19398 + 5.19398i −3.82598 + 3.82598i −0.768954 14.3940i
34.20 2.34575 + 2.34575i −3.89202 7.00508i −6.20731 6.20731i −9.12970 9.12970i −4.51214 + 4.51214i −7.04916 + 7.04916i 6.14781 29.1216i
See all 44 embeddings
\(n\): e.g. 2-40 or 990-1000
Embeddings: e.g. 1-3 or 34.22
Significant digits:
Format:

Inner twists

Char Parity Ord Mult Type
1.a even 1 1 trivial
13.d odd 4 1 inner

Twists

       By twisting character orbit
Char Parity Ord Mult Type Twist Min Dim
1.a even 1 1 trivial 143.3.f.a 44
13.d odd 4 1 inner 143.3.f.a 44
    
        By twisted newform orbit
Twist Min Dim Char Parity Ord Mult Type
143.3.f.a 44 1.a even 1 1 trivial
143.3.f.a 44 13.d odd 4 1 inner

Hecke kernels

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