Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [819,2,Mod(467,819)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(819, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([3, 5, 3]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("819.467");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 819 = 3^{2} \cdot 7 \cdot 13 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 819.ci (of order \(6\), degree \(2\), 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: | \(6.53974792554\) |
Analytic rank: | \(0\) |
Dimension: | \(72\) |
Relative dimension: | \(36\) over \(\Q(\zeta_{6})\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
$q$-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 | \( a_{2} \) | \( a_{3} \) | \( a_{4} \) | \( a_{5} \) | \( a_{6} \) | \( a_{7} \) | \( a_{8} \) | \( a_{9} \) | \( a_{10} \) | ||||||||||||||||||
---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
467.1 | −1.37968 | + | 2.38967i | 0 | −2.80702 | − | 4.86190i | 1.99090 | + | 1.14945i | 0 | −1.91747 | + | 1.82300i | 9.97241 | 0 | −5.49360 | + | 3.17173i | ||||||||
467.2 | −1.37968 | + | 2.38967i | 0 | −2.80702 | − | 4.86190i | 1.99090 | + | 1.14945i | 0 | 1.91747 | − | 1.82300i | 9.97241 | 0 | −5.49360 | + | 3.17173i | ||||||||
467.3 | −1.09409 | + | 1.89502i | 0 | −1.39405 | − | 2.41457i | −0.641017 | − | 0.370091i | 0 | −2.56351 | − | 0.654522i | 1.72452 | 0 | 1.40266 | − | 0.809824i | ||||||||
467.4 | −1.09409 | + | 1.89502i | 0 | −1.39405 | − | 2.41457i | −0.641017 | − | 0.370091i | 0 | 2.56351 | + | 0.654522i | 1.72452 | 0 | 1.40266 | − | 0.809824i | ||||||||
467.5 | −1.08917 | + | 1.88649i | 0 | −1.37256 | − | 2.37735i | −2.98264 | − | 1.72203i | 0 | −1.35636 | + | 2.27162i | 1.62313 | 0 | 6.49718 | − | 3.75115i | ||||||||
467.6 | −1.08917 | + | 1.88649i | 0 | −1.37256 | − | 2.37735i | −2.98264 | − | 1.72203i | 0 | 1.35636 | − | 2.27162i | 1.62313 | 0 | 6.49718 | − | 3.75115i | ||||||||
467.7 | −0.968539 | + | 1.67756i | 0 | −0.876135 | − | 1.51751i | 1.13052 | + | 0.652705i | 0 | −2.20198 | − | 1.46673i | −0.479871 | 0 | −2.18990 | + | 1.26434i | ||||||||
467.8 | −0.968539 | + | 1.67756i | 0 | −0.876135 | − | 1.51751i | 1.13052 | + | 0.652705i | 0 | 2.20198 | + | 1.46673i | −0.479871 | 0 | −2.18990 | + | 1.26434i | ||||||||
467.9 | −0.780978 | + | 1.35269i | 0 | −0.219854 | − | 0.380798i | 1.39160 | + | 0.803439i | 0 | −0.416239 | + | 2.61280i | −2.43711 | 0 | −2.17361 | + | 1.25494i | ||||||||
467.10 | −0.780978 | + | 1.35269i | 0 | −0.219854 | − | 0.380798i | 1.39160 | + | 0.803439i | 0 | 0.416239 | − | 2.61280i | −2.43711 | 0 | −2.17361 | + | 1.25494i | ||||||||
467.11 | −0.549318 | + | 0.951447i | 0 | 0.396499 | + | 0.686757i | −3.41932 | − | 1.97415i | 0 | −1.06953 | − | 2.41994i | −3.06849 | 0 | 3.75659 | − | 2.16887i | ||||||||
467.12 | −0.549318 | + | 0.951447i | 0 | 0.396499 | + | 0.686757i | −3.41932 | − | 1.97415i | 0 | 1.06953 | + | 2.41994i | −3.06849 | 0 | 3.75659 | − | 2.16887i | ||||||||
467.13 | −0.468702 | + | 0.811816i | 0 | 0.560636 | + | 0.971050i | 2.67694 | + | 1.54553i | 0 | −0.745969 | + | 2.53841i | −2.92590 | 0 | −2.50937 | + | 1.44879i | ||||||||
467.14 | −0.468702 | + | 0.811816i | 0 | 0.560636 | + | 0.971050i | 2.67694 | + | 1.54553i | 0 | 0.745969 | − | 2.53841i | −2.92590 | 0 | −2.50937 | + | 1.44879i | ||||||||
467.15 | −0.377074 | + | 0.653111i | 0 | 0.715630 | + | 1.23951i | −1.10552 | − | 0.638272i | 0 | −2.40470 | − | 1.10336i | −2.58768 | 0 | 0.833725 | − | 0.481351i | ||||||||
467.16 | −0.377074 | + | 0.653111i | 0 | 0.715630 | + | 1.23951i | −1.10552 | − | 0.638272i | 0 | 2.40470 | + | 1.10336i | −2.58768 | 0 | 0.833725 | − | 0.481351i | ||||||||
467.17 | −0.0396259 | + | 0.0686340i | 0 | 0.996860 | + | 1.72661i | 1.56036 | + | 0.900875i | 0 | −2.37846 | + | 1.15885i | −0.316509 | 0 | −0.123661 | + | 0.0713959i | ||||||||
467.18 | −0.0396259 | + | 0.0686340i | 0 | 0.996860 | + | 1.72661i | 1.56036 | + | 0.900875i | 0 | 2.37846 | − | 1.15885i | −0.316509 | 0 | −0.123661 | + | 0.0713959i | ||||||||
467.19 | 0.0396259 | − | 0.0686340i | 0 | 0.996860 | + | 1.72661i | −1.56036 | − | 0.900875i | 0 | −2.37846 | + | 1.15885i | 0.316509 | 0 | −0.123661 | + | 0.0713959i | ||||||||
467.20 | 0.0396259 | − | 0.0686340i | 0 | 0.996860 | + | 1.72661i | −1.56036 | − | 0.900875i | 0 | 2.37846 | − | 1.15885i | 0.316509 | 0 | −0.123661 | + | 0.0713959i | ||||||||
See all 72 embeddings |
Inner twists
Char | Parity | Ord | Mult | Type |
---|---|---|---|---|
1.a | even | 1 | 1 | trivial |
3.b | odd | 2 | 1 | inner |
7.d | odd | 6 | 1 | inner |
13.b | even | 2 | 1 | inner |
21.g | even | 6 | 1 | inner |
39.d | odd | 2 | 1 | inner |
91.s | odd | 6 | 1 | inner |
273.ba | even | 6 | 1 | inner |
Twists
By twisting character orbit | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Mult | Type | Twist | Min | Dim |
1.a | even | 1 | 1 | trivial | 819.2.ci.a | ✓ | 72 |
3.b | odd | 2 | 1 | inner | 819.2.ci.a | ✓ | 72 |
7.d | odd | 6 | 1 | inner | 819.2.ci.a | ✓ | 72 |
13.b | even | 2 | 1 | inner | 819.2.ci.a | ✓ | 72 |
21.g | even | 6 | 1 | inner | 819.2.ci.a | ✓ | 72 |
39.d | odd | 2 | 1 | inner | 819.2.ci.a | ✓ | 72 |
91.s | odd | 6 | 1 | inner | 819.2.ci.a | ✓ | 72 |
273.ba | even | 6 | 1 | inner | 819.2.ci.a | ✓ | 72 |
By twisted newform orbit | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Mult | Type |
819.2.ci.a | ✓ | 72 | 1.a | even | 1 | 1 | trivial |
819.2.ci.a | ✓ | 72 | 3.b | odd | 2 | 1 | inner |
819.2.ci.a | ✓ | 72 | 7.d | odd | 6 | 1 | inner |
819.2.ci.a | ✓ | 72 | 13.b | even | 2 | 1 | inner |
819.2.ci.a | ✓ | 72 | 21.g | even | 6 | 1 | inner |
819.2.ci.a | ✓ | 72 | 39.d | odd | 2 | 1 | inner |
819.2.ci.a | ✓ | 72 | 91.s | odd | 6 | 1 | inner |
819.2.ci.a | ✓ | 72 | 273.ba | even | 6 | 1 | inner |
Hecke kernels
This newform subspace is the entire newspace \(S_{2}^{\mathrm{new}}(819, [\chi])\).