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Properties

Label 143.4.h.b
Level $143$
Weight $4$
Character orbit 143.h
Analytic conductor $8.437$
Analytic rank $0$
Dimension $76$
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: \(76\)
Relative dimension: \(19\) 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.

\(\operatorname{Tr}(f)(q) = \) \( 76 q + 4 q^{2} - 12 q^{3} - 148 q^{4} - 16 q^{5} + 77 q^{6} + 56 q^{7} - 34 q^{8} - 241 q^{9}+O(q^{10}) \) Copy content Toggle raw display
\(\operatorname{Tr}(f)(q) = \) \( 76 q + 4 q^{2} - 12 q^{3} - 148 q^{4} - 16 q^{5} + 77 q^{6} + 56 q^{7} - 34 q^{8} - 241 q^{9} + 60 q^{10} - 47 q^{11} + 244 q^{12} + 247 q^{13} + 117 q^{14} - 2 q^{15} + 212 q^{16} - 344 q^{17} - 461 q^{18} - 59 q^{19} + 55 q^{20} - 296 q^{21} - 76 q^{22} + 1680 q^{23} + 784 q^{24} - 89 q^{25} + 13 q^{26} - 309 q^{27} - 654 q^{28} - 306 q^{29} + 606 q^{30} + 344 q^{31} - 2408 q^{32} + 1265 q^{33} - 116 q^{34} + 934 q^{35} - 3571 q^{36} + 188 q^{37} - 9 q^{38} + 91 q^{39} - 1803 q^{40} + 1518 q^{41} + 1734 q^{42} - 966 q^{43} + 1513 q^{44} + 2272 q^{45} - 165 q^{46} - 2146 q^{47} + 2320 q^{48} - 2085 q^{49} - 71 q^{50} - 501 q^{51} + 1924 q^{52} + 814 q^{53} - 6546 q^{54} - 1924 q^{55} + 6538 q^{56} - 1099 q^{57} - 4169 q^{58} - 41 q^{59} - 2812 q^{60} + 1788 q^{61} - 3931 q^{62} + 4980 q^{63} + 4256 q^{64} - 1352 q^{65} - 1543 q^{66} + 9878 q^{67} + 648 q^{68} - 2994 q^{69} + 6094 q^{70} - 612 q^{71} + 2965 q^{72} + 3436 q^{73} + 2616 q^{74} + 5089 q^{75} - 6632 q^{76} - 2604 q^{77} + 2704 q^{78} - 7688 q^{79} - 11093 q^{80} - 3972 q^{81} + 1076 q^{82} + 2007 q^{83} - 5729 q^{84} - 2128 q^{85} + 2433 q^{86} + 1812 q^{87} - 9006 q^{88} + 7454 q^{89} - 2204 q^{90} - 728 q^{91} + 2143 q^{92} - 8158 q^{93} + 4055 q^{94} + 824 q^{95} + 811 q^{96} + 5711 q^{97} - 4086 q^{98} - 11439 q^{99}+O(q^{100}) \) 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 −3.97940 + 2.89120i 1.95471 + 6.01598i 5.00442 − 15.4020i −11.7650 − 8.54779i −25.1720 − 18.2885i 3.34037 − 10.2806i 12.4558 + 38.3350i −10.5277 + 7.64881i 71.5310
14.2 −3.86396 + 2.80733i −2.15852 − 6.64323i 4.57694 − 14.0864i 15.1953 + 11.0400i 26.9902 + 19.6095i 5.98138 − 18.4088i 10.0528 + 30.9394i −17.6298 + 12.8088i −89.7068
14.3 −3.52735 + 2.56277i −2.18335 − 6.71965i 3.40227 − 10.4711i −10.8529 − 7.88510i 24.9223 + 18.1071i 8.14177 − 25.0578i 4.05543 + 12.4813i −18.5432 + 13.4724i 58.4897
14.4 −2.91090 + 2.11489i −0.259273 − 0.797959i 1.52843 − 4.70403i 11.0738 + 8.04557i 2.44232 + 1.77445i −4.53569 + 13.9594i −3.39551 − 10.4503i 21.2739 − 15.4564i −49.2501
14.5 −2.72658 + 1.98097i 0.202439 + 0.623042i 1.03782 − 3.19409i −5.78677 − 4.20434i −1.78619 − 1.29775i −10.4846 + 32.2682i −4.83397 − 14.8774i 21.4963 − 15.6179i 24.1068
14.6 −1.83784 + 1.33527i 3.01069 + 9.26595i −0.877420 + 2.70042i −5.97680 − 4.34240i −17.9057 − 13.0093i 4.55364 − 14.0147i −7.60918 − 23.4186i −54.9500 + 39.9235i 16.7827
14.7 −1.16976 + 0.849884i 0.145177 + 0.446808i −1.82609 + 5.62012i −0.581588 − 0.422548i −0.549558 − 0.399277i 9.00894 − 27.7267i −6.21484 − 19.1273i 21.6649 − 15.7405i 1.03944
14.8 −1.00764 + 0.732094i −2.29028 − 7.04876i −1.99276 + 6.13307i −17.2161 − 12.5082i 7.46814 + 5.42592i −3.51372 + 10.8141i −5.56108 − 17.1153i −22.5962 + 16.4171i 26.5048
14.9 −0.471643 + 0.342668i −1.46721 − 4.51561i −2.36711 + 7.28522i 1.58259 + 1.14982i 2.23936 + 1.62699i −0.116501 + 0.358552i −2.82120 − 8.68275i 3.60544 − 2.61951i −1.14042
14.10 −0.367022 + 0.266657i 2.05644 + 6.32908i −2.40854 + 7.41271i 4.33326 + 3.14829i −2.44245 − 1.77455i −8.57944 + 26.4048i −2.21419 − 6.81457i −13.9848 + 10.1606i −2.42992
14.11 0.778995 − 0.565973i 2.31474 + 7.12403i −2.18563 + 6.72667i 14.4838 + 10.5231i 5.83518 + 4.23951i 7.91022 − 24.3451i 4.48492 + 13.8032i −23.5504 + 17.1103i 17.2386
14.12 1.29329 − 0.939630i −2.72994 − 8.40189i −1.68244 + 5.17803i 12.6344 + 9.17944i −11.4253 − 8.30094i −8.06287 + 24.8150i 6.64148 + 20.4404i −41.2957 + 30.0031i 24.9652
14.13 1.57062 − 1.14112i 0.990304 + 3.04784i −1.30744 + 4.02390i −16.0734 − 11.6780i 5.03336 + 3.65695i 8.77337 − 27.0017i 7.33766 + 22.5830i 13.5348 − 9.83362i −38.5714
14.14 2.37777 − 1.72755i 0.497021 + 1.52967i 0.197213 − 0.606958i 2.32261 + 1.68747i 3.82439 + 2.77858i −3.54970 + 10.9248i 6.68618 + 20.5780i 19.7506 − 14.3496i 8.43781
14.15 2.81215 − 2.04314i 2.92761 + 9.01025i 1.26159 − 3.88278i −15.8411 − 11.5093i 26.6421 + 19.3566i −7.78834 + 23.9700i 4.20786 + 12.9505i −50.7703 + 36.8868i −68.0627
14.16 3.22629 − 2.34404i −0.854707 − 2.63052i 2.44231 − 7.51667i 11.3312 + 8.23261i −8.92357 − 6.48335i 6.77683 − 20.8569i 0.118933 + 0.366039i 15.6544 − 11.3736i 55.8554
14.17 3.35922 − 2.44061i −2.65195 − 8.16188i 2.85561 − 8.78865i −4.97791 − 3.61667i −28.8285 − 20.9451i −0.679316 + 2.09072i −1.59225 − 4.90045i −37.7399 + 27.4196i −25.5488
14.18 4.28022 − 3.10976i 2.69766 + 8.30254i 6.17752 − 19.0125i 8.55907 + 6.21853i 37.3655 + 27.1476i 1.51239 − 4.65465i −19.6039 − 60.3345i −39.8113 + 28.9246i 55.9728
14.19 4.28158 − 3.11075i 0.388610 + 1.19602i 6.18303 − 19.0294i −9.86077 − 7.16427i 5.38439 + 3.91199i −3.63304 + 11.1813i −19.6393 − 60.4435i 20.5640 − 14.9406i −64.5059
27.1 −1.72974 − 5.32359i 3.50563 + 2.54699i −18.8765 + 13.7146i −2.86043 + 8.80351i 7.49531 − 23.0682i 15.0972 − 10.9687i 69.4343 + 50.4470i −2.54117 − 7.82093i 51.8141
See all 76 embeddings
\(n\): e.g. 2-40 or 990-1000
Embeddings: e.g. 1-3 or 14.19
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.b ✓ 76
11.c even 5 1 inner 143.4.h.b ✓ 76
11.c even 5 1 1573.4.a.q 38
11.d odd 10 1 1573.4.a.r 38
    
        By twisted newform orbit
Twist Min Dim Char Parity Ord Mult Type
143.4.h.b ✓ 76 1.a even 1 1 trivial
143.4.h.b ✓ 76 11.c even 5 1 inner
1573.4.a.q 38 11.c even 5 1
1573.4.a.r 38 11.d odd 10 1

Hecke kernels

This newform subspace can be constructed as the kernel of the linear operator \( T_{2}^{76} - 4 T_{2}^{75} + 158 T_{2}^{74} - 594 T_{2}^{73} + 13147 T_{2}^{72} - 45392 T_{2}^{71} + \cdots + 12\!\cdots\!96 \) acting on \(S_{4}^{\mathrm{new}}(143, [\chi])\). Copy content Toggle raw display