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.
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) |
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 \(S_{5}^{\mathrm{new}}(95, [\chi])\).