Properties

Label 95.4.p.a
Level $95$
Weight $4$
Character orbit 95.p
Analytic conductor $5.605$
Analytic rank $0$
Dimension $168$
Inner twists $4$

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Newspace parameters

Copy content comment:Compute space of new eigenforms
 
Copy content gp:[N,k,chi] = [95,4,Mod(4,95)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)
 
Copy content magma:// Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("95.4"); S:= CuspForms(chi, 4); N := Newforms(S);
 
Copy content sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(95, base_ring=CyclotomicField(18)) chi = DirichletCharacter(H, H._module([9, 2])) N = Newforms(chi, 4, names="a")
 
Level: \( N \) \(=\) \( 95 = 5 \cdot 19 \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 95.p (of order \(18\), degree \(6\), minimal)

Newform invariants

Copy content comment:select newform
 
Copy content sage:traces = [] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(0)] == traces)
 
Copy content gp:f = lf[1] \\ Warning: the index may be different
 
Self dual: no
Analytic conductor: \(5.60518145055\)
Analytic rank: \(0\)
Dimension: \(168\)
Relative dimension: \(28\) over \(\Q(\zeta_{18})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{18}]$

$q$-expansion

The algebraic \(q\)-expansion of this newform has not been computed, but we have computed the trace expansion.

\(\operatorname{Tr}(f)(q) = \) \( 168 q + 6 q^{4} - 6 q^{5} + 6 q^{6} - 12 q^{9} + 3 q^{10} - 90 q^{11} + 162 q^{14} - 72 q^{15} + 426 q^{16} - 444 q^{19} - 966 q^{20} + 114 q^{21} + 108 q^{24} + 270 q^{25} - 642 q^{26} - 60 q^{29} + 396 q^{30}+ \cdots + 22692 q^{99}+O(q^{100}) \) Copy content Toggle raw display

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.

Copy content comment:embeddings in the coefficient field
 
Copy content gp:mfembed(f)
 
Label   \( a_{2} \) \( a_{3} \) \( a_{4} \) \( a_{5} \) \( a_{6} \) \( a_{7} \) \( a_{8} \) \( a_{9} \) \( a_{10} \)
4.1 −1.90265 + 5.22750i 5.97212 − 1.05305i −17.5783 − 14.7500i −10.6702 − 3.33861i −5.85808 + 33.2228i −9.66735 − 5.58145i 72.0093 − 41.5746i 9.18560 − 3.34328i 37.7544 − 49.4264i
4.2 −1.83075 + 5.02994i −6.67395 + 1.17680i −15.8203 − 13.2748i 6.58809 + 9.03311i 6.29910 − 35.7240i −23.1341 − 13.3565i 58.6494 − 33.8613i 17.7851 − 6.47325i −57.4971 + 16.6004i
4.3 −1.58557 + 4.35631i 3.81534 − 0.672747i −10.3350 − 8.67213i 10.0879 − 4.82027i −3.11878 + 17.6875i 17.2154 + 9.93930i 22.0470 − 12.7289i −11.2675 + 4.10102i 5.00362 + 51.5887i
4.4 −1.54939 + 4.25691i −6.49006 + 1.14437i −9.59232 − 8.04891i −4.06396 − 10.4156i 5.18413 − 29.4007i 13.9343 + 8.04499i 17.7402 − 10.2423i 15.4395 − 5.61953i 50.6348 − 1.16216i
4.5 −1.40644 + 3.86417i 0.235273 − 0.0414849i −6.82541 − 5.72720i −2.66370 + 10.8584i −0.170593 + 0.967481i 14.0326 + 8.10175i 3.24050 − 1.87090i −25.3181 + 9.21502i −38.2124 − 25.5647i
4.6 −1.17190 + 3.21976i −1.04177 + 0.183692i −2.86517 − 2.40416i 8.45885 − 7.31080i 0.629403 − 3.56952i −30.3869 − 17.5439i −12.6403 + 7.29787i −24.3202 + 8.85181i 13.6261 + 35.8030i
4.7 −1.15144 + 3.16356i 8.44720 − 1.48947i −2.55395 − 2.14302i −1.08681 + 11.1274i −5.01443 + 28.4383i −14.7094 − 8.49249i −13.6041 + 7.85435i 43.7649 − 15.9291i −33.9508 − 16.2507i
4.8 −0.941187 + 2.58589i 1.61091 − 0.284046i 0.327359 + 0.274686i −9.82466 − 5.33630i −0.781651 + 4.43297i −13.1699 − 7.60364i −20.0838 + 11.5954i −22.8574 + 8.31940i 23.0459 − 20.3830i
4.9 −0.854996 + 2.34908i 9.69690 − 1.70982i 1.34119 + 1.12539i −0.825464 − 11.1498i −4.27429 + 24.2407i 12.3819 + 7.14868i −21.1097 + 12.1877i 65.7346 − 23.9254i 26.8976 + 7.59397i
4.10 −0.811338 + 2.22913i −8.50321 + 1.49935i 1.81760 + 1.52514i −9.66250 + 5.62459i 3.55674 − 20.1713i −5.98741 − 3.45683i −21.3095 + 12.3030i 44.6849 − 16.2640i −4.69840 − 26.1024i
4.11 −0.692404 + 1.90236i −6.05130 + 1.06701i 2.98879 + 2.50789i 10.3565 + 4.21218i 2.16011 − 12.2506i 14.4781 + 8.35896i −20.8662 + 12.0471i 10.1080 − 3.67902i −15.1840 + 16.7853i
4.12 −0.358626 + 0.985318i 4.97216 − 0.876727i 5.28612 + 4.43558i 8.56332 + 7.18815i −0.919294 + 5.21358i 1.32457 + 0.764739i −13.5308 + 7.81200i −1.41794 + 0.516087i −10.1536 + 5.85973i
4.13 −0.163864 + 0.450212i 2.51249 − 0.443020i 5.95252 + 4.99475i −11.1258 + 1.10321i −0.212253 + 1.20375i 24.1826 + 13.9618i −6.54343 + 3.77785i −19.2554 + 7.00838i 1.32643 − 5.18973i
4.14 −0.108808 + 0.298949i −4.85373 + 0.855843i 6.05082 + 5.07724i 4.62275 − 10.1799i 0.272273 − 1.54414i 5.90230 + 3.40770i −4.38032 + 2.52898i −2.54550 + 0.926487i 2.54027 + 2.48962i
4.15 0.108808 − 0.298949i 4.85373 − 0.855843i 6.05082 + 5.07724i 10.8280 − 2.78480i 0.272273 − 1.54414i −5.90230 − 3.40770i 4.38032 − 2.52898i −2.54550 + 0.926487i 0.345662 − 3.54002i
4.16 0.163864 − 0.450212i −2.51249 + 0.443020i 5.95252 + 4.99475i −3.01843 + 10.7652i −0.212253 + 1.20375i −24.1826 − 13.9618i 6.54343 − 3.77785i −19.2554 + 7.00838i 4.35200 + 3.12295i
4.17 0.358626 − 0.985318i −4.97216 + 0.876727i 5.28612 + 4.43558i −5.59194 − 9.68144i −0.919294 + 5.21358i −1.32457 − 0.764739i 13.5308 − 7.81200i −1.41794 + 0.516087i −11.5447 + 2.03782i
4.18 0.692404 − 1.90236i 6.05130 − 1.06701i 2.98879 + 2.50789i −2.34979 − 10.9306i 2.16011 − 12.2506i −14.4781 − 8.35896i 20.8662 − 12.0471i 10.1080 − 3.67902i −22.4210 − 3.09824i
4.19 0.811338 − 2.22913i 8.50321 − 1.49935i 1.81760 + 1.52514i −7.21702 + 8.53901i 3.55674 − 20.1713i 5.98741 + 3.45683i 21.3095 − 12.3030i 44.6849 − 16.2640i 13.1791 + 23.0157i
4.20 0.854996 − 2.34908i −9.69690 + 1.70982i 1.34119 + 1.12539i 10.8371 + 2.74907i −4.27429 + 24.2407i −12.3819 − 7.14868i 21.1097 − 12.1877i 65.7346 − 23.9254i 15.7235 − 23.1068i
See next 80 embeddings (of 168 total)
\(n\): e.g. 2-40 or 80-90
Embeddings: e.g. 1-3 or 4.28
Significant digits:
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Inner twists

Char Parity Ord Mult Type
1.a even 1 1 trivial
5.b even 2 1 inner
19.e even 9 1 inner
95.p even 18 1 inner

Twists

       By twisting character orbit
Char Parity Ord Mult Type Twist Min Dim
1.a even 1 1 trivial 95.4.p.a ✓ 168
5.b even 2 1 inner 95.4.p.a ✓ 168
19.e even 9 1 inner 95.4.p.a ✓ 168
95.p even 18 1 inner 95.4.p.a ✓ 168
    
        By twisted newform orbit
Twist Min Dim Char Parity Ord Mult Type
95.4.p.a ✓ 168 1.a even 1 1 trivial
95.4.p.a ✓ 168 5.b even 2 1 inner
95.4.p.a ✓ 168 19.e even 9 1 inner
95.4.p.a ✓ 168 95.p even 18 1 inner

Hecke kernels

This newform subspace is the entire newspace \(S_{4}^{\mathrm{new}}(95, [\chi])\).