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Properties

Label 143.4.h.a
Level $143$
Weight $4$
Character orbit 143.h
Analytic conductor $8.437$
Analytic rank $0$
Dimension $68$
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(14,143)]
 
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([8, 0]))
 
N = Newforms(chi, 4, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("143.14");
 
S:= CuspForms(chi, 4);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 143 = 11 \cdot 13 \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 143.h (of order \(5\), 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: \(8.43727313082\)
Analytic rank: \(0\)
Dimension: \(68\)
Relative dimension: \(17\) over \(\Q(\zeta_{5})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{5}]$

$q$-expansion

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

\(\operatorname{Tr}(f)(q) = \) \( 68 q + 4 q^{2} + 12 q^{3} - 16 q^{4} + 24 q^{5} + 7 q^{6} + 8 q^{7} - 34 q^{8} - 55 q^{9}+O(q^{10}) \) Copy content Toggle raw display
\(\operatorname{Tr}(f)(q) = \) \( 68 q + 4 q^{2} + 12 q^{3} - 16 q^{4} + 24 q^{5} + 7 q^{6} + 8 q^{7} - 34 q^{8} - 55 q^{9} - 36 q^{10} - 51 q^{11} - 524 q^{12} - 221 q^{13} + 133 q^{14} + 178 q^{15} - 140 q^{16} + 302 q^{17} + 575 q^{18} - 59 q^{19} + 73 q^{20} - 136 q^{21} - 196 q^{22} - 1264 q^{23} + 224 q^{24} - 603 q^{25} - 13 q^{26} - 45 q^{27} + 948 q^{28} + 916 q^{29} - 90 q^{30} + 160 q^{31} + 1752 q^{32} + 713 q^{33} - 1204 q^{34} - 582 q^{35} + 373 q^{36} - 692 q^{37} + 663 q^{38} + 221 q^{39} + 1293 q^{40} - 2 q^{41} - 1782 q^{42} + 698 q^{43} + 897 q^{44} - 2048 q^{45} - 3385 q^{46} + 1754 q^{47} - 3944 q^{48} - 1579 q^{49} + 1061 q^{50} + 1103 q^{51} - 208 q^{52} + 1354 q^{53} + 6262 q^{54} + 3556 q^{55} - 3350 q^{56} + 1765 q^{57} + 819 q^{58} - 217 q^{59} + 228 q^{60} - 1632 q^{61} - 823 q^{62} + 352 q^{63} - 6388 q^{64} - 728 q^{65} + 6541 q^{66} - 6426 q^{67} + 1688 q^{68} + 486 q^{69} - 6242 q^{70} + 2988 q^{71} - 2073 q^{72} + 2116 q^{73} - 3120 q^{74} - 5631 q^{75} + 4008 q^{76} + 5450 q^{77} + 936 q^{78} + 4520 q^{79} + 2955 q^{80} - 6210 q^{81} + 6592 q^{82} - 641 q^{83} + 517 q^{84} - 1856 q^{85} - 3869 q^{86} + 1924 q^{87} + 4998 q^{88} - 7266 q^{89} + 6420 q^{90} + 104 q^{91} - 1429 q^{92} + 7114 q^{93} + 1427 q^{94} - 708 q^{95} + 8925 q^{96} - 3725 q^{97} - 2974 q^{98} + 7833 q^{99}+O(q^{100}) \) 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   \( a_{2} \) \( a_{3} \) \( a_{4} \) \( a_{5} \) \( a_{6} \) \( a_{7} \) \( a_{8} \) \( a_{9} \) \( a_{10} \)
14.1 −4.43083 + 3.21918i −1.61795 − 4.97954i 6.79695 − 20.9189i −1.77922 − 1.29268i 23.1989 + 16.8550i −7.95857 + 24.4940i 23.6862 + 72.8985i −0.334627 + 0.243121i 12.0448
14.2 −3.47986 + 2.52827i −0.669520 − 2.06057i 3.24516 − 9.98758i −8.81271 − 6.40281i 7.53951 + 5.47777i 1.33129 − 4.09730i 3.32506 + 10.2335i 18.0458 − 13.1110i 46.8550
14.3 −3.01508 + 2.19058i 2.64240 + 8.13246i 1.81991 − 5.60111i 9.33768 + 6.78422i −25.7819 − 18.7316i −3.65701 + 11.2551i −2.43074 − 7.48105i −37.3112 + 27.1082i −43.0152
14.4 −2.45816 + 1.78596i 0.944462 + 2.90676i 0.380774 − 1.17190i 6.23533 + 4.53024i −7.51299 − 5.45850i 9.62984 − 29.6376i −6.35451 − 19.5572i 14.2862 − 10.3796i −23.4183
14.5 −2.23637 + 1.62482i −2.82465 − 8.69339i −0.110814 + 0.341050i 3.43743 + 2.49744i 20.4422 + 14.8521i −5.09482 + 15.6802i −7.14007 − 21.9749i −45.7528 + 33.2414i −11.7453
14.6 −1.95153 + 1.41787i 1.17190 + 3.60673i −0.674012 + 2.07439i −13.9051 − 10.1026i −7.40089 − 5.37706i −2.26259 + 6.96352i −7.58923 − 23.3573i 10.2083 − 7.41675i 41.4606
14.7 −1.92631 + 1.39955i −1.97595 − 6.08135i −0.720198 + 2.21654i 4.29934 + 3.12365i 12.3174 + 8.94913i 1.64214 − 5.05400i −7.60110 − 23.3938i −11.2350 + 8.16270i −12.6535
14.8 −0.400584 + 0.291041i 0.225252 + 0.693255i −2.39637 + 7.37528i 16.7143 + 12.1437i −0.291998 − 0.212149i −2.65028 + 8.15671i −2.41064 − 7.41918i 21.4136 − 15.5579i −10.2298
14.9 −0.0253892 + 0.0184463i 1.76760 + 5.44013i −2.47183 + 7.60752i −6.11234 − 4.44088i −0.145228 − 0.105515i −1.91554 + 5.89541i −0.155155 − 0.477519i −4.62709 + 3.36178i 0.237105
14.10 1.06952 − 0.777051i −2.87269 − 8.84124i −1.93207 + 5.94631i −4.88097 − 3.54623i −9.94250 − 7.22365i 11.1335 − 34.2654i 5.82236 + 17.9194i −48.0717 + 34.9261i −7.97590
14.11 1.64125 − 1.19244i −1.40236 − 4.31601i −1.20034 + 3.69426i 9.87094 + 7.17166i −7.44820 − 5.41143i 3.82371 − 11.7682i 7.45035 + 22.9298i 5.18214 − 3.76505i 24.7525
14.12 1.88993 − 1.37311i −1.38946 − 4.27631i −0.785744 + 2.41827i −10.3395 − 7.51211i −8.49785 − 6.17405i −10.5881 + 32.5869i 7.61067 + 23.4232i 5.48720 − 3.98669i −29.8560
14.13 2.24227 − 1.62910i 2.35875 + 7.25948i −0.0983427 + 0.302668i 3.65722 + 2.65713i 17.1154 + 12.4351i 0.863031 − 2.65614i 7.12433 + 21.9264i −25.2928 + 18.3763i 12.5292
14.14 3.57314 − 2.59604i −1.21298 − 3.73318i 3.55578 − 10.9436i −10.5709 − 7.68024i −14.0256 − 10.1902i 2.06707 − 6.36178i −4.78609 − 14.7301i 9.37817 − 6.81364i −57.7097
14.15 3.57791 − 2.59950i 0.693568 + 2.13458i 3.57187 − 10.9931i 11.6383 + 8.45575i 8.03038 + 5.83441i −10.3864 + 31.9661i −4.86361 − 14.9687i 17.7680 − 12.9092i 63.6217
14.16 3.62344 − 2.63258i 1.38748 + 4.27021i 3.72667 − 11.4695i −3.97822 − 2.89035i 16.2691 + 11.8202i 8.08076 − 24.8700i −5.61882 − 17.2930i 5.53385 − 4.02058i −22.0239
14.17 4.42470 − 3.21473i −2.05208 − 6.31565i 6.77132 − 20.8400i 10.1327 + 7.36185i −29.3829 − 21.3480i −1.00225 + 3.08462i −23.5132 − 72.3663i −13.8329 + 10.0502i 68.5006
27.1 −1.47502 − 4.53963i −3.70948 − 2.69510i −11.9604 + 8.68976i −2.80173 + 8.62283i −6.76320 + 20.8150i −9.62173 + 6.99059i 26.1970 + 19.0332i −1.84675 − 5.68371i 43.2770
27.2 −1.38998 − 4.27791i 7.41235 + 5.38539i −9.89632 + 7.19010i 4.49878 − 13.8458i 12.7352 − 39.1949i 11.1788 − 8.12190i 15.4022 + 11.1903i 17.5971 + 54.1583i −65.4843
27.3 −1.34438 − 4.13757i 0.689758 + 0.501138i −8.84001 + 6.42264i 1.46848 − 4.51952i 1.14620 − 3.52764i 7.20065 − 5.23158i 10.3014 + 7.48443i −8.11883 − 24.9872i −20.6740
See all 68 embeddings
\(n\): e.g. 2-40 or 990-1000
Embeddings: e.g. 1-3 or 14.17
Significant digits:
Format:

Inner twists

Char Parity Ord Mult Type
1.a even 1 1 trivial
11.c even 5 1 inner

Twists

       By twisting character orbit
Char Parity Ord Mult Type Twist Min Dim
1.a even 1 1 trivial 143.4.h.a ✓ 68
11.c even 5 1 inner 143.4.h.a ✓ 68
11.c even 5 1 1573.4.a.o 34
11.d odd 10 1 1573.4.a.p 34
    
        By twisted newform orbit
Twist Min Dim Char Parity Ord Mult Type
143.4.h.a ✓ 68 1.a even 1 1 trivial
143.4.h.a ✓ 68 11.c even 5 1 inner
1573.4.a.o 34 11.c even 5 1
1573.4.a.p 34 11.d odd 10 1

Hecke kernels

This newform subspace can be constructed as the kernel of the linear operator \( T_{2}^{68} - 4 T_{2}^{67} + 84 T_{2}^{66} - 298 T_{2}^{65} + 4505 T_{2}^{64} - 14468 T_{2}^{63} + \cdots + 27\!\cdots\!00 \) acting on \(S_{4}^{\mathrm{new}}(143, [\chi])\). Copy content Toggle raw display