Properties

Label 95.5.o.a
Level $95$
Weight $5$
Character orbit 95.o
Analytic conductor $9.820$
Analytic rank $0$
Dimension $228$
Inner twists $4$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [95,5,Mod(14,95)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(95, base_ring=CyclotomicField(18))
 
chi = DirichletCharacter(H, H._module([9, 7]))
 
N = Newforms(chi, 5, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("95.14");
 
S:= CuspForms(chi, 5);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 95 = 5 \cdot 19 \)
Weight: \( k \) \(=\) \( 5 \)
Character orbit: \([\chi]\) \(=\) 95.o (of order \(18\), degree \(6\), 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: \(9.82014649297\)
Analytic rank: \(0\)
Dimension: \(228\)
Relative dimension: \(38\) 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.

\(\operatorname{Tr}(f)(q) = \) \( 228 q + 30 q^{4} - 6 q^{5} + 42 q^{6} - 12 q^{9} + 291 q^{10} + 84 q^{11} + 738 q^{14} + 1113 q^{15} - 1974 q^{16} - 900 q^{19} - 570 q^{20} + 1878 q^{21} - 5988 q^{24} + 804 q^{25} - 3678 q^{26} - 1992 q^{29}+ \cdots + 99978 q^{99}+O(q^{100}) \) 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.

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 −7.40788 + 2.69625i 1.50123 8.51389i 35.3503 29.6624i 19.1235 + 16.1025i 11.8346 + 67.1176i 48.2711 27.8693i −118.827 + 205.814i 5.88243 + 2.14103i −185.081 67.7236i
14.2 −6.85393 + 2.49463i −1.18769 + 6.73573i 28.4965 23.9114i −6.83155 24.0485i −8.66278 49.1290i −5.21093 + 3.00853i −77.3124 + 133.909i 32.1557 + 11.7037i 106.815 + 147.784i
14.3 −6.59628 + 2.40085i 1.76326 9.99994i 25.4901 21.3887i −24.8912 2.32933i 12.3774 + 70.1957i −67.6958 + 39.0842i −60.6317 + 105.017i −20.7746 7.56132i 169.782 44.3952i
14.4 −6.30314 + 2.29415i −2.50071 + 14.1822i 22.2097 18.6361i 21.5603 + 12.6551i −16.7739 95.1296i −34.1936 + 19.7417i −43.5752 + 75.4745i −118.767 43.2278i −164.931 30.3040i
14.5 −6.01483 + 2.18922i −1.70858 + 9.68986i 19.1288 16.0509i −18.9127 + 16.3496i −10.9364 62.0233i 51.8511 29.9363i −28.7104 + 49.7279i −14.8591 5.40828i 77.9641 139.744i
14.6 −5.38533 + 1.96010i 0.134961 0.765405i 12.9031 10.8270i −4.75926 + 24.5428i 0.773457 + 4.38649i −13.6434 + 7.87703i −2.41778 + 4.18772i 75.5475 + 27.4970i −22.4762 141.500i
14.7 −5.25244 + 1.91173i 1.32959 7.54046i 11.6767 9.79789i 16.0384 19.1773i 7.43176 + 42.1476i 13.5268 7.80969i 2.11618 3.66533i 21.0244 + 7.65224i −47.5786 + 131.389i
14.8 −4.78309 + 1.74090i 2.47898 14.0590i 7.59047 6.36916i −23.6297 8.16323i 12.6181 + 71.5610i 77.2210 44.5835i 15.5026 26.8513i −115.395 42.0002i 127.234 2.09151i
14.9 −4.69065 + 1.70726i −0.376165 + 2.13334i 6.83074 5.73167i 24.8552 2.68712i −1.87770 10.6489i −59.2774 + 34.2238i 17.6783 30.6197i 71.7055 + 26.0987i −111.999 + 55.0385i
14.10 −4.13554 + 1.50522i 2.93140 16.6248i 2.58034 2.16516i 11.8864 + 21.9935i 12.9010 + 73.1649i −30.6629 + 17.7033i 27.7956 48.1433i −191.675 69.7641i −82.2616 73.0635i
14.11 −3.52100 + 1.28154i −2.38693 + 13.5369i −1.50162 + 1.26001i −24.8719 + 2.52724i −8.94374 50.7225i −52.6413 + 30.3925i 33.6482 58.2804i −101.436 36.9197i 84.3353 40.7728i
14.12 −3.39457 + 1.23552i −2.98573 + 16.9329i −2.26011 + 1.89646i 11.3403 22.2800i −10.7857 61.1689i 41.3710 23.8855i 34.2284 59.2854i −201.694 73.4105i −10.9680 + 89.6422i
14.13 −3.32147 + 1.20892i −0.561583 + 3.18489i −2.68603 + 2.25385i −13.3325 21.1482i −1.98499 11.2574i 35.4163 20.4476i 34.4739 59.7106i 66.2869 + 24.1265i 69.8498 + 54.1251i
14.14 −2.73358 + 0.994941i −0.907478 + 5.14656i −5.77418 + 4.84511i 21.4580 + 12.8279i −2.63986 14.9714i 62.9116 36.3221i 34.2357 59.2979i 50.4515 + 18.3629i −71.4201 13.7165i
14.15 −2.20060 + 0.800951i 0.827041 4.69038i −8.05561 + 6.75946i −12.1567 + 21.8453i 1.93678 + 10.9840i −12.9426 + 7.47242i 31.0477 53.7763i 54.7994 + 19.9454i 9.25487 57.8095i
14.16 −1.76722 + 0.643217i 0.450057 2.55240i −9.54736 + 8.01119i −23.7268 7.87656i 0.846396 + 4.80015i −35.6783 + 20.5989i 26.7645 46.3575i 69.8029 + 25.4062i 46.9968 1.34181i
14.17 −1.25162 + 0.455552i 2.23018 12.6480i −10.8977 + 9.14425i 0.690830 24.9905i 2.97048 + 16.8464i −46.3047 + 26.7340i 20.1296 34.8656i −78.8829 28.7110i 10.5198 + 31.5932i
14.18 −0.534639 + 0.194593i −1.62464 + 9.21380i −12.0087 + 10.0765i 13.8462 20.8155i −0.924341 5.24220i −55.4052 + 31.9882i 9.01113 15.6077i −6.13953 2.23461i −3.35215 + 13.8231i
14.19 −0.0826234 + 0.0300725i 1.85499 10.5202i −12.2508 + 10.2796i 24.9603 + 1.40757i 0.163102 + 0.924996i 26.5076 15.3042i 1.40648 2.43609i −31.1178 11.3260i −2.10464 + 0.634321i
14.20 0.0826234 0.0300725i −1.85499 + 10.5202i −12.2508 + 10.2796i 5.72050 + 24.3367i 0.163102 + 0.924996i −26.5076 + 15.3042i −1.40648 + 2.43609i −31.1178 11.3260i 1.20451 + 1.83875i
See next 80 embeddings (of 228 total)
\(n\): e.g. 2-40 or 990-1000
Embeddings: e.g. 1-3 or 14.38
Significant digits:
Format:

Inner twists

Char Parity Ord Mult Type
1.a even 1 1 trivial
5.b even 2 1 inner
19.f odd 18 1 inner
95.o odd 18 1 inner

Twists

       By twisting character orbit
Char Parity Ord Mult Type Twist Min Dim
1.a even 1 1 trivial 95.5.o.a 228
5.b even 2 1 inner 95.5.o.a 228
19.f odd 18 1 inner 95.5.o.a 228
95.o odd 18 1 inner 95.5.o.a 228
    
        By twisted newform orbit
Twist Min Dim Char Parity Ord Mult Type
95.5.o.a 228 1.a even 1 1 trivial
95.5.o.a 228 5.b even 2 1 inner
95.5.o.a 228 19.f odd 18 1 inner
95.5.o.a 228 95.o odd 18 1 inner

Hecke kernels

This newform subspace is the entire newspace \(S_{5}^{\mathrm{new}}(95, [\chi])\).