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Properties

Label 143.4.e.b
Level $143$
Weight $4$
Character orbit 143.e
Analytic conductor $8.437$
Analytic rank $0$
Dimension $34$
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] = [143,4,Mod(100,143)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(143, base_ring=CyclotomicField(6))
 
chi = DirichletCharacter(H, H._module([0, 4]))
 
N = Newforms(chi, 4, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("143.100");
 
S:= CuspForms(chi, 4);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 143 = 11 \cdot 13 \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 143.e (of order \(3\), 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: \(8.43727313082\)
Analytic rank: \(0\)
Dimension: \(34\)
Relative dimension: \(17\) over \(\Q(\zeta_{3})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

$q$-expansion

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

\(\operatorname{Tr}(f)(q) = \) \( 34 q + 6 q^{3} - 50 q^{4} - 48 q^{5} - 16 q^{6} + 62 q^{7} - 42 q^{8} - 135 q^{9}+O(q^{10}) \) Copy content Toggle raw display
\(\operatorname{Tr}(f)(q) = \) \( 34 q + 6 q^{3} - 50 q^{4} - 48 q^{5} - 16 q^{6} + 62 q^{7} - 42 q^{8} - 135 q^{9} - 2 q^{10} - 187 q^{11} - 254 q^{12} + 76 q^{13} + 148 q^{15} - 126 q^{16} + 74 q^{17} + 180 q^{18} + 159 q^{19} + 222 q^{20} - 368 q^{21} + 215 q^{23} - 214 q^{24} + 190 q^{25} + 123 q^{26} - 384 q^{27} + 358 q^{28} + 157 q^{29} - 829 q^{30} - 788 q^{31} + 553 q^{32} + 66 q^{33} - 1404 q^{34} - 58 q^{35} + 700 q^{36} - 88 q^{37} - 2636 q^{38} + 798 q^{39} + 1466 q^{40} + 512 q^{41} - 337 q^{42} - 927 q^{43} + 1100 q^{44} + 1482 q^{45} + 1361 q^{46} - 286 q^{47} + 178 q^{48} - 1835 q^{49} + 583 q^{50} - 1136 q^{51} + 2306 q^{52} + 212 q^{53} + 67 q^{54} + 264 q^{55} - 2059 q^{56} + 2596 q^{57} + 1690 q^{58} + 266 q^{59} + 74 q^{60} + 624 q^{61} - 643 q^{62} + 2360 q^{63} - 3178 q^{64} + 470 q^{65} + 352 q^{66} + 676 q^{67} + 413 q^{68} - 764 q^{69} - 2122 q^{70} + 763 q^{71} + 1366 q^{72} - 4748 q^{73} + 1649 q^{74} - 2420 q^{75} + 2101 q^{76} - 1364 q^{77} - 5848 q^{78} + 4328 q^{79} + 1013 q^{80} - 537 q^{81} - 3152 q^{82} + 1554 q^{83} + 3381 q^{84} + 1690 q^{85} + 5788 q^{86} + 4200 q^{87} + 231 q^{88} + 1687 q^{89} - 10798 q^{90} - 3380 q^{91} + 11084 q^{92} + 4310 q^{93} - 1777 q^{94} - 1124 q^{95} - 6930 q^{96} + 2047 q^{97} - 1553 q^{98} + 2970 q^{99}+O(q^{100}) \) 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   \( a_{2} \) \( a_{3} \) \( a_{4} \) \( a_{5} \) \( a_{6} \) \( a_{7} \) \( a_{8} \) \( a_{9} \) \( a_{10} \)
100.1 −2.55759 + 4.42988i 1.79098 − 3.10206i −9.08257 − 15.7315i −2.16776 9.16117 + 15.8676i −10.4904 − 18.1698i 51.9966 7.08482 + 12.2713i 5.54425 − 9.60293i
100.2 −2.09541 + 3.62936i −2.35272 + 4.07503i −4.78153 − 8.28185i 14.4259 −9.85985 − 17.0778i 17.3506 + 30.0521i 6.55048 2.42942 + 4.20788i −30.2283 + 52.3570i
100.3 −2.07785 + 3.59895i −3.58804 + 6.21467i −4.63495 − 8.02797i −11.1721 −14.9108 − 25.8263i 3.89211 + 6.74134i 5.27734 −12.2481 − 21.2143i 23.2141 − 40.2080i
100.4 −2.06912 + 3.58383i 2.73933 − 4.74466i −4.56254 − 7.90254i −3.23279 11.3360 + 19.6346i −1.53684 − 2.66188i 4.65582 −1.50786 − 2.61170i 6.68904 − 11.5858i
100.5 −1.39209 + 2.41118i 4.47320 − 7.74782i 0.124146 + 0.215028i −17.0433 12.4542 + 21.5714i 15.4676 + 26.7907i −22.9648 −26.5191 − 45.9324i 23.7259 − 41.0944i
100.6 −0.944521 + 1.63596i −0.783201 + 1.35654i 2.21576 + 3.83781i 2.20557 −1.47950 − 2.56257i 0.902360 + 1.56293i −23.4837 12.2732 + 21.2578i −2.08320 + 3.60821i
100.7 −0.706890 + 1.22437i −2.88255 + 4.99273i 3.00061 + 5.19721i −4.58681 −4.07530 − 7.05862i −18.2120 − 31.5441i −19.7947 −3.11823 − 5.40093i 3.24237 − 5.61595i
100.8 −0.495908 + 0.858937i 2.68049 − 4.64275i 3.50815 + 6.07630i 18.5970 2.65856 + 4.60475i 6.70244 + 11.6090i −14.8934 −0.870106 − 1.50707i −9.22237 + 15.9736i
100.9 0.315613 − 0.546657i −4.62136 + 8.00442i 3.80078 + 6.58314i −19.0524 2.91712 + 5.05260i 12.7218 + 22.0348i 9.84810 −29.2139 − 50.5999i −6.01317 + 10.4151i
100.10 0.332082 − 0.575182i 0.423352 − 0.733267i 3.77944 + 6.54619i −8.92433 −0.281175 − 0.487009i −1.76528 − 3.05755i 10.3336 13.1415 + 22.7618i −2.96360 + 5.13311i
100.11 0.534214 − 0.925286i 4.92554 − 8.53128i 3.42923 + 5.93960i 2.35929 −5.26259 − 9.11507i −6.12528 − 10.6093i 15.8752 −35.0219 − 60.6597i 1.26037 − 2.18302i
100.12 0.856937 − 1.48426i −3.79109 + 6.56636i 2.53132 + 4.38437i 12.0244 6.49745 + 11.2539i −0.574325 − 0.994761i 22.3877 −15.2447 − 26.4047i 10.3041 − 17.8473i
100.13 1.56350 − 2.70806i 0.268802 − 0.465578i −0.889055 − 1.53989i −0.516265 −0.840543 − 1.45586i 17.3210 + 30.0008i 19.4558 13.3555 + 23.1324i −0.807180 + 1.39808i
100.14 1.58752 − 2.74967i 0.300230 − 0.520013i −1.04047 − 1.80214i 12.4679 −0.953244 − 1.65107i −5.31270 − 9.20186i 18.7933 13.3197 + 23.0704i 19.7931 − 34.2827i
100.15 2.05606 − 3.56120i 2.00775 − 3.47753i −4.45478 − 7.71591i −12.3424 −8.25614 − 14.3001i −14.8185 − 25.6664i −3.74025 5.43784 + 9.41862i −25.3768 + 43.9540i
100.16 2.54066 − 4.40055i 3.69680 − 6.40305i −8.90987 − 15.4324i 8.39690 −18.7846 − 32.5359i 7.09626 + 12.2911i −49.8972 −13.8327 − 23.9589i 21.3336 − 36.9509i
100.17 2.55281 − 4.42160i −2.28752 + 3.96210i −9.03368 − 15.6468i −15.4387 11.6792 + 20.2290i 8.38111 + 14.5165i −51.4001 3.03450 + 5.25591i −39.4122 + 68.2639i
133.1 −2.55759 − 4.42988i 1.79098 + 3.10206i −9.08257 + 15.7315i −2.16776 9.16117 − 15.8676i −10.4904 + 18.1698i 51.9966 7.08482 − 12.2713i 5.54425 + 9.60293i
133.2 −2.09541 − 3.62936i −2.35272 − 4.07503i −4.78153 + 8.28185i 14.4259 −9.85985 + 17.0778i 17.3506 − 30.0521i 6.55048 2.42942 − 4.20788i −30.2283 − 52.3570i
133.3 −2.07785 − 3.59895i −3.58804 − 6.21467i −4.63495 + 8.02797i −11.1721 −14.9108 + 25.8263i 3.89211 − 6.74134i 5.27734 −12.2481 + 21.2143i 23.2141 + 40.2080i
See all 34 embeddings
\(n\): e.g. 2-40 or 990-1000
Embeddings: e.g. 1-3 or 100.17
Significant digits:
Format:

Inner twists

Char Parity Ord Mult Type
1.a even 1 1 trivial
13.c even 3 1 inner

Twists

       By twisting character orbit
Char Parity Ord Mult Type Twist Min Dim
1.a even 1 1 trivial 143.4.e.b ✓ 34
13.c even 3 1 inner 143.4.e.b ✓ 34
13.c even 3 1 1859.4.a.g 17
13.e even 6 1 1859.4.a.h 17
    
        By twisted newform orbit
Twist Min Dim Char Parity Ord Mult Type
143.4.e.b ✓ 34 1.a even 1 1 trivial
143.4.e.b ✓ 34 13.c even 3 1 inner
1859.4.a.g 17 13.c even 3 1
1859.4.a.h 17 13.e even 6 1

Hecke kernels

This newform subspace can be constructed as the kernel of the linear operator \( T_{2}^{34} + 93 T_{2}^{32} + 14 T_{2}^{31} + 5200 T_{2}^{30} + 1057 T_{2}^{29} + 190322 T_{2}^{28} + \cdots + 4887141433344 \) acting on \(S_{4}^{\mathrm{new}}(143, [\chi])\). Copy content Toggle raw display