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Properties

Label 143.3.c.a
Level $143$
Weight $3$
Character orbit 143.c
Analytic conductor $3.896$
Analytic rank $0$
Dimension $24$
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(131,143)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(143, base_ring=CyclotomicField(2))
 
chi = DirichletCharacter(H, H._module([1, 0]))
 
N = Newforms(chi, 3, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("143.131");
 
S:= CuspForms(chi, 3);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 143 = 11 \cdot 13 \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 143.c (of order \(2\), degree \(1\), 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: \(24\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

$q$-expansion

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

\(\operatorname{Tr}(f)(q) = \) \( 24 q + 6 q^{3} - 60 q^{4} - 2 q^{5} + 38 q^{9}+O(q^{10}) \) Copy content Toggle raw display
\(\operatorname{Tr}(f)(q) = \) \( 24 q + 6 q^{3} - 60 q^{4} - 2 q^{5} + 38 q^{9} + 14 q^{11} - 8 q^{12} - 20 q^{14} - 66 q^{15} + 124 q^{16} + 16 q^{20} + 4 q^{22} - 110 q^{23} + 190 q^{25} + 18 q^{27} + 42 q^{31} - 190 q^{33} - 80 q^{34} - 142 q^{36} + 82 q^{37} + 6 q^{38} - 206 q^{42} + 52 q^{44} - 56 q^{45} - 16 q^{47} + 338 q^{48} - 400 q^{49} + 236 q^{53} - 34 q^{55} + 338 q^{56} + 308 q^{58} - 230 q^{59} + 116 q^{60} - 100 q^{64} - 218 q^{66} + 162 q^{67} - 54 q^{69} + 268 q^{70} - 318 q^{71} + 72 q^{75} + 444 q^{77} + 130 q^{78} - 584 q^{80} - 204 q^{81} - 52 q^{82} - 864 q^{86} + 268 q^{88} + 70 q^{89} + 104 q^{91} + 430 q^{92} + 474 q^{93} + 122 q^{97} + 216 q^{99}+O(q^{100}) \) 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   \( a_{2} \) \( a_{3} \) \( a_{4} \) \( a_{5} \) \( a_{6} \) \( a_{7} \) \( a_{8} \) \( a_{9} \) \( a_{10} \)
131.1 − 3.76286i 3.59245 −10.1591 −8.98890 − 13.5179i − 5.39510i 23.1758i 3.90572 33.8239i
131.2 − 3.69281i −2.06358 −9.63682 1.14598 7.62041i 10.3077i 20.8157i −4.74163 − 4.23188i
131.3 − 3.55214i 0.917654 −8.61771 7.59428 − 3.25964i − 12.8216i 16.4028i −8.15791 − 26.9760i
131.4 − 3.14662i −5.05103 −5.90125 −3.48341 15.8937i − 4.34583i 5.98251i 16.5129 10.9610i
131.5 − 2.99206i 4.76628 −4.95241 4.46470 − 14.2610i 6.91883i 2.84966i 13.7174 − 13.3586i
131.6 − 2.26440i −0.295394 −1.12750 −8.07495 0.668889i 2.72544i − 6.50448i −8.91274 18.2849i
131.7 − 2.21699i −1.66196 −0.915028 1.22050 3.68453i − 5.75137i − 6.83934i −6.23791 − 2.70583i
131.8 − 2.01808i 3.37255 −0.0726456 −0.285019 − 6.80608i 1.31198i − 7.92571i 2.37410 0.575191i
131.9 − 1.96318i −4.37958 0.145939 8.78169 8.59790i 8.63704i − 8.13921i 10.1808 − 17.2400i
131.10 − 0.658957i 1.15850 3.56578 5.96734 − 0.763399i 2.95957i − 4.98552i −7.65789 − 3.93222i
131.11 − 0.550174i 4.67776 3.69731 −4.62409 − 2.57358i − 11.4688i − 4.23486i 12.8814 2.54406i
131.12 − 0.162945i −2.03366 3.97345 −4.71812 0.331375i 12.8210i − 1.29924i −4.86424 0.768796i
131.13 0.162945i −2.03366 3.97345 −4.71812 − 0.331375i − 12.8210i 1.29924i −4.86424 − 0.768796i
131.14 0.550174i 4.67776 3.69731 −4.62409 2.57358i 11.4688i 4.23486i 12.8814 − 2.54406i
131.15 0.658957i 1.15850 3.56578 5.96734 0.763399i − 2.95957i 4.98552i −7.65789 3.93222i
131.16 1.96318i −4.37958 0.145939 8.78169 − 8.59790i − 8.63704i 8.13921i 10.1808 17.2400i
131.17 2.01808i 3.37255 −0.0726456 −0.285019 6.80608i − 1.31198i 7.92571i 2.37410 − 0.575191i
131.18 2.21699i −1.66196 −0.915028 1.22050 − 3.68453i 5.75137i 6.83934i −6.23791 2.70583i
131.19 2.26440i −0.295394 −1.12750 −8.07495 − 0.668889i − 2.72544i 6.50448i −8.91274 − 18.2849i
131.20 2.99206i 4.76628 −4.95241 4.46470 14.2610i − 6.91883i − 2.84966i 13.7174 13.3586i
See all 24 embeddings
\(n\): e.g. 2-40 or 990-1000
Embeddings: e.g. 1-3 or 131.24
Significant digits:
Format:

Inner twists

Char Parity Ord Mult Type
1.a even 1 1 trivial
11.b odd 2 1 inner

Twists

       By twisting character orbit
Char Parity Ord Mult Type Twist Min Dim
1.a even 1 1 trivial 143.3.c.a ✓ 24
11.b odd 2 1 inner 143.3.c.a ✓ 24
    
        By twisted newform orbit
Twist Min Dim Char Parity Ord Mult Type
143.3.c.a ✓ 24 1.a even 1 1 trivial
143.3.c.a ✓ 24 11.b odd 2 1 inner

Hecke kernels

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