Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [190,3,Mod(21,190)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(190, base_ring=CyclotomicField(18))
chi = DirichletCharacter(H, H._module([0, 1]))
N = Newforms(chi, 3, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("190.21");
S:= CuspForms(chi, 3);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 190 = 2 \cdot 5 \cdot 19 \) |
Weight: | \( k \) | \(=\) | \( 3 \) |
Character orbit: | \([\chi]\) | \(=\) | 190.n (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: | \(5.17712502285\) |
Analytic rank: | \(0\) |
Dimension: | \(72\) |
Relative dimension: | \(12\) over \(\Q(\zeta_{18})\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{18}]$ |
$q$-expansion
The dimension is sufficiently large that we do not compute an algebraic \(q\)-expansion, 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 | \( a_{2} \) | \( a_{3} \) | \( a_{4} \) | \( a_{5} \) | \( a_{6} \) | \( a_{7} \) | \( a_{8} \) | \( a_{9} \) | \( a_{10} \) | ||||||||||||||||||
---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
21.1 | −1.39273 | − | 0.245576i | −2.57446 | + | 3.06812i | 1.87939 | + | 0.684040i | 2.10122 | − | 0.764780i | 4.33898 | − | 3.64084i | −5.04257 | − | 8.73399i | −2.44949 | − | 1.41421i | −1.22270 | − | 6.93427i | −3.11424 | + | 0.549124i |
21.2 | −1.39273 | − | 0.245576i | −1.67774 | + | 1.99946i | 1.87939 | + | 0.684040i | −2.10122 | + | 0.764780i | 2.82766 | − | 2.37269i | −1.31266 | − | 2.27359i | −2.44949 | − | 1.41421i | 0.379829 | + | 2.15412i | 3.11424 | − | 0.549124i |
21.3 | −1.39273 | − | 0.245576i | 1.03536 | − | 1.23389i | 1.87939 | + | 0.684040i | −2.10122 | + | 0.764780i | −1.74498 | + | 1.46421i | 2.41544 | + | 4.18367i | −2.44949 | − | 1.41421i | 1.11231 | + | 6.30824i | 3.11424 | − | 0.549124i |
21.4 | −1.39273 | − | 0.245576i | 1.36309 | − | 1.62446i | 1.87939 | + | 0.684040i | 2.10122 | − | 0.764780i | −2.29734 | + | 1.92769i | 5.37129 | + | 9.30334i | −2.44949 | − | 1.41421i | 0.781958 | + | 4.43471i | −3.11424 | + | 0.549124i |
21.5 | −1.39273 | − | 0.245576i | 2.70607 | − | 3.22497i | 1.87939 | + | 0.684040i | −2.10122 | + | 0.764780i | −4.56079 | + | 3.82696i | −1.23095 | − | 2.13207i | −2.44949 | − | 1.41421i | −1.51477 | − | 8.59068i | 3.11424 | − | 0.549124i |
21.6 | −1.39273 | − | 0.245576i | 3.27506 | − | 3.90306i | 1.87939 | + | 0.684040i | 2.10122 | − | 0.764780i | −5.51976 | + | 4.63163i | −4.65931 | − | 8.07016i | −2.44949 | − | 1.41421i | −2.94505 | − | 16.7022i | −3.11424 | + | 0.549124i |
21.7 | 1.39273 | + | 0.245576i | −1.59995 | + | 1.90675i | 1.87939 | + | 0.684040i | −2.10122 | + | 0.764780i | −2.69655 | + | 2.26268i | 0.787505 | + | 1.36400i | 2.44949 | + | 1.41421i | 0.486987 | + | 2.76184i | −3.11424 | + | 0.549124i |
21.8 | 1.39273 | + | 0.245576i | −1.37923 | + | 1.64370i | 1.87939 | + | 0.684040i | 2.10122 | − | 0.764780i | −2.32454 | + | 1.95052i | 1.70226 | + | 2.94840i | 2.44949 | + | 1.41421i | 0.763353 | + | 4.32919i | 3.11424 | − | 0.549124i |
21.9 | 1.39273 | + | 0.245576i | 0.639869 | − | 0.762566i | 1.87939 | + | 0.684040i | −2.10122 | + | 0.764780i | 1.07843 | − | 0.904911i | 4.68265 | + | 8.11058i | 2.44949 | + | 1.41421i | 1.39076 | + | 7.88739i | −3.11424 | + | 0.549124i |
21.10 | 1.39273 | + | 0.245576i | 1.44897 | − | 1.72682i | 1.87939 | + | 0.684040i | 2.10122 | − | 0.764780i | 2.44209 | − | 2.04915i | −6.09672 | − | 10.5598i | 2.44949 | + | 1.41421i | 0.680457 | + | 3.85906i | 3.11424 | − | 0.549124i |
21.11 | 1.39273 | + | 0.245576i | 2.62535 | − | 3.12877i | 1.87939 | + | 0.684040i | 2.10122 | − | 0.764780i | 4.42475 | − | 3.71280i | 3.48073 | + | 6.02881i | 2.44949 | + | 1.41421i | −1.33391 | − | 7.56496i | 3.11424 | − | 0.549124i |
21.12 | 1.39273 | + | 0.245576i | 3.65518 | − | 4.35607i | 1.87939 | + | 0.684040i | −2.10122 | + | 0.764780i | 6.16041 | − | 5.16920i | −2.18145 | − | 3.77837i | 2.44949 | + | 1.41421i | −4.05220 | − | 22.9811i | −3.11424 | + | 0.549124i |
41.1 | −0.909039 | + | 1.08335i | −1.22181 | − | 3.35689i | −0.347296 | − | 1.96962i | 0.388289 | − | 2.20210i | 4.74736 | + | 1.72790i | −3.45517 | − | 5.98452i | 2.44949 | + | 1.41421i | −2.88148 | + | 2.41785i | 2.03267 | + | 2.42245i |
41.2 | −0.909039 | + | 1.08335i | −1.03511 | − | 2.84395i | −0.347296 | − | 1.96962i | −0.388289 | + | 2.20210i | 4.02195 | + | 1.46387i | 1.78310 | + | 3.08842i | 2.44949 | + | 1.41421i | −0.122188 | + | 0.102527i | −2.03267 | − | 2.42245i |
41.3 | −0.909039 | + | 1.08335i | 0.00657243 | + | 0.0180576i | −0.347296 | − | 1.96962i | −0.388289 | + | 2.20210i | −0.0255373 | − | 0.00929482i | 1.70435 | + | 2.95202i | 2.44949 | + | 1.41421i | 6.89412 | − | 5.78485i | −2.03267 | − | 2.42245i |
41.4 | −0.909039 | + | 1.08335i | 0.585942 | + | 1.60986i | −0.347296 | − | 1.96962i | 0.388289 | − | 2.20210i | −2.27669 | − | 0.828647i | −3.14961 | − | 5.45529i | 2.44949 | + | 1.41421i | 4.64607 | − | 3.89852i | 2.03267 | + | 2.42245i |
41.5 | −0.909039 | + | 1.08335i | 1.52962 | + | 4.20261i | −0.347296 | − | 1.96962i | 0.388289 | − | 2.20210i | −5.94339 | − | 2.16322i | 3.75037 | + | 6.49584i | 2.44949 | + | 1.41421i | −8.42777 | + | 7.07174i | 2.03267 | + | 2.42245i |
41.6 | −0.909039 | + | 1.08335i | 1.92230 | + | 5.28147i | −0.347296 | − | 1.96962i | −0.388289 | + | 2.20210i | −7.46913 | − | 2.71854i | −5.56528 | − | 9.63935i | 2.44949 | + | 1.41421i | −17.3043 | + | 14.5201i | −2.03267 | − | 2.42245i |
41.7 | 0.909039 | − | 1.08335i | −1.74791 | − | 4.80234i | −0.347296 | − | 1.96962i | −0.388289 | + | 2.20210i | −6.79154 | − | 2.47192i | −3.09091 | − | 5.35361i | −2.44949 | − | 1.41421i | −13.1129 | + | 11.0030i | 2.03267 | + | 2.42245i |
41.8 | 0.909039 | − | 1.08335i | −1.27347 | − | 3.49882i | −0.347296 | − | 1.96962i | 0.388289 | − | 2.20210i | −4.94808 | − | 1.80095i | −1.30839 | − | 2.26620i | −2.44949 | − | 1.41421i | −3.72564 | + | 3.12618i | −2.03267 | − | 2.42245i |
See all 72 embeddings |
Inner twists
Char | Parity | Ord | Mult | Type |
---|---|---|---|---|
1.a | even | 1 | 1 | trivial |
19.f | odd | 18 | 1 | inner |
Twists
By twisting character orbit | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Mult | Type | Twist | Min | Dim |
1.a | even | 1 | 1 | trivial | 190.3.n.a | ✓ | 72 |
19.f | odd | 18 | 1 | inner | 190.3.n.a | ✓ | 72 |
By twisted newform orbit | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Mult | Type |
190.3.n.a | ✓ | 72 | 1.a | even | 1 | 1 | trivial |
190.3.n.a | ✓ | 72 | 19.f | odd | 18 | 1 | inner |
Hecke kernels
This newform subspace is the entire newspace \(S_{3}^{\mathrm{new}}(190, [\chi])\).