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Properties

Label 143.3.l.a
Level $143$
Weight $3$
Character orbit 143.l
Analytic conductor $3.896$
Analytic rank $0$
Dimension $104$
CM no
Inner twists $4$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [143,3,Mod(51,143)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(143, base_ring=CyclotomicField(10))
 
chi = DirichletCharacter(H, H._module([7, 5]))
 
N = Newforms(chi, 3, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("143.51");
 
S:= CuspForms(chi, 3);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 143 = 11 \cdot 13 \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 143.l (of order \(10\), degree \(4\), 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: \(104\)
Relative dimension: \(26\) over \(\Q(\zeta_{10})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{10}]$

$q$-expansion

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

\(\operatorname{Tr}(f)(q) = \) \( 104 q - 6 q^{3} - 54 q^{4} - 84 q^{9}+O(q^{10}) \) Copy content Toggle raw display
\(\operatorname{Tr}(f)(q) = \) \( 104 q - 6 q^{3} - 54 q^{4} - 84 q^{9} + 12 q^{12} - 20 q^{13} + 58 q^{14} + 14 q^{16} - 50 q^{17} + 38 q^{22} - 76 q^{23} + 168 q^{25} - 108 q^{26} + 42 q^{27} - 180 q^{29} + 140 q^{30} - 160 q^{35} - 338 q^{36} - 318 q^{38} + 260 q^{39} + 150 q^{40} + 556 q^{42} + 212 q^{48} + 56 q^{49} + 570 q^{51} - 310 q^{52} + 148 q^{53} - 270 q^{55} - 532 q^{56} - 150 q^{61} - 150 q^{62} + 82 q^{64} - 242 q^{66} + 660 q^{68} + 348 q^{69} - 660 q^{74} - 818 q^{75} - 418 q^{77} + 860 q^{78} - 570 q^{79} + 544 q^{81} + 642 q^{82} + 554 q^{88} + 280 q^{90} - 266 q^{91} - 922 q^{92} + 210 q^{94} - 810 q^{95}+O(q^{100}) \) 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   \( a_{2} \) \( a_{3} \) \( a_{4} \) \( a_{5} \) \( a_{6} \) \( a_{7} \) \( a_{8} \) \( a_{9} \) \( a_{10} \)
51.1 −3.02144 − 2.19520i 0.585572 − 1.80220i 3.07410 + 9.46111i −1.75733 − 2.41876i −5.72548 + 4.15980i 2.66422 + 8.19964i 6.86451 − 21.1268i 4.37610 + 3.17943i 11.1658i
51.2 −2.82004 − 2.04888i −1.25043 + 3.84842i 2.51865 + 7.75162i 2.50890 + 3.45320i 11.4112 − 8.29073i −0.223021 − 0.686388i 4.47079 − 13.7597i −5.96564 − 4.33429i − 14.8786i
51.3 −2.69106 − 1.95517i 0.176677 − 0.543756i 2.18306 + 6.71876i 1.31649 + 1.81200i −1.53859 + 1.11785i −2.01615 − 6.20507i 3.15001 − 9.69474i 7.01670 + 5.09793i − 7.45018i
51.4 −2.53158 − 1.83930i 1.79129 − 5.51303i 1.78981 + 5.50847i 2.04665 + 2.81697i −14.6749 + 10.6620i −1.62857 − 5.01222i 1.73278 − 5.33294i −19.9036 − 14.4608i − 10.8958i
51.5 −2.25418 − 1.63776i −1.32492 + 4.07767i 1.16300 + 3.57935i −4.45588 − 6.13300i 9.66482 − 7.02190i 3.28279 + 10.1034i −0.203584 + 0.626566i −7.59083 − 5.51506i 21.1225i
51.6 −1.94391 − 1.41233i −0.995690 + 3.06442i 0.548029 + 1.68666i −1.34642 − 1.85319i 6.26351 − 4.55070i −2.19645 − 6.75997i −1.65322 + 5.08809i −1.11811 − 0.812354i 5.50401i
51.7 −1.67236 − 1.21504i 0.504421 − 1.55245i 0.0843999 + 0.259756i 2.56632 + 3.53223i −2.72986 + 1.98336i 4.03619 + 12.4221i −2.38067 + 7.32696i 5.12550 + 3.72389i − 9.02535i
51.8 −1.67025 − 1.21350i 1.24324 − 3.82631i 0.0810591 + 0.249474i −4.54363 − 6.25378i −6.71976 + 4.88219i −0.679454 − 2.09114i −2.38456 + 7.33892i −5.81384 − 4.22400i 15.9591i
51.9 −1.50448 − 1.09307i 0.270406 − 0.832225i −0.167409 − 0.515232i 5.40136 + 7.43434i −1.31650 + 0.956492i −1.15895 − 3.56688i −2.60996 + 8.03263i 6.66167 + 4.83999i − 17.0889i
51.10 −1.17852 − 0.856242i −0.0260343 + 0.0801253i −0.580319 − 1.78604i −2.92699 − 4.02865i 0.0992885 − 0.0721373i −0.860540 − 2.64847i −2.64598 + 8.14348i 7.27541 + 5.28590i 7.25404i
51.11 −0.701560 − 0.509713i −1.69693 + 5.22260i −1.00369 − 3.08904i 4.52524 + 6.22845i 3.85252 − 2.79902i 0.768444 + 2.36503i −1.94226 + 5.97767i −17.1148 − 12.4347i − 6.67621i
51.12 −0.0873087 − 0.0634334i 1.26555 − 3.89496i −1.23247 − 3.79315i 1.60106 + 2.20367i −0.357564 + 0.259786i −1.65109 − 5.08152i −0.266403 + 0.819904i −6.28795 − 4.56847i − 0.293961i
51.13 −0.0831281 − 0.0603961i −0.734152 + 2.25949i −1.23281 − 3.79418i −0.264220 − 0.363668i 0.197493 − 0.143487i 3.05071 + 9.38911i −0.253682 + 0.780752i 2.71485 + 1.97245i 0.0461889i
51.14 0.0831281 + 0.0603961i −0.734152 + 2.25949i −1.23281 − 3.79418i 0.264220 + 0.363668i −0.197493 + 0.143487i −3.05071 − 9.38911i 0.253682 − 0.780752i 2.71485 + 1.97245i 0.0461889i
51.15 0.0873087 + 0.0634334i 1.26555 − 3.89496i −1.23247 − 3.79315i −1.60106 − 2.20367i 0.357564 − 0.259786i 1.65109 + 5.08152i 0.266403 − 0.819904i −6.28795 − 4.56847i − 0.293961i
51.16 0.701560 + 0.509713i −1.69693 + 5.22260i −1.00369 − 3.08904i −4.52524 − 6.22845i −3.85252 + 2.79902i −0.768444 − 2.36503i 1.94226 − 5.97767i −17.1148 − 12.4347i − 6.67621i
51.17 1.17852 + 0.856242i −0.0260343 + 0.0801253i −0.580319 − 1.78604i 2.92699 + 4.02865i −0.0992885 + 0.0721373i 0.860540 + 2.64847i 2.64598 − 8.14348i 7.27541 + 5.28590i 7.25404i
51.18 1.50448 + 1.09307i 0.270406 − 0.832225i −0.167409 − 0.515232i −5.40136 − 7.43434i 1.31650 − 0.956492i 1.15895 + 3.56688i 2.60996 − 8.03263i 6.66167 + 4.83999i − 17.0889i
51.19 1.67025 + 1.21350i 1.24324 − 3.82631i 0.0810591 + 0.249474i 4.54363 + 6.25378i 6.71976 − 4.88219i 0.679454 + 2.09114i 2.38456 − 7.33892i −5.81384 − 4.22400i 15.9591i
51.20 1.67236 + 1.21504i 0.504421 − 1.55245i 0.0843999 + 0.259756i −2.56632 − 3.53223i 2.72986 − 1.98336i −4.03619 − 12.4221i 2.38067 − 7.32696i 5.12550 + 3.72389i − 9.02535i
See next 80 embeddings (of 104 total)
\(n\): e.g. 2-40 or 990-1000
Embeddings: e.g. 1-3 or 51.26
Significant digits:
Format:

Inner twists

Char Parity Ord Mult Type
1.a even 1 1 trivial
11.d odd 10 1 inner
13.b even 2 1 inner
143.l 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.l.a ✓ 104
11.d odd 10 1 inner 143.3.l.a ✓ 104
13.b even 2 1 inner 143.3.l.a ✓ 104
143.l odd 10 1 inner 143.3.l.a ✓ 104
    
        By twisted newform orbit
Twist Min Dim Char Parity Ord Mult Type
143.3.l.a ✓ 104 1.a even 1 1 trivial
143.3.l.a ✓ 104 11.d odd 10 1 inner
143.3.l.a ✓ 104 13.b even 2 1 inner
143.3.l.a ✓ 104 143.l odd 10 1 inner

Hecke kernels

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