Properties

Label 819.2.ci.a
Level $819$
Weight $2$
Character orbit 819.ci
Analytic conductor $6.540$
Analytic rank $0$
Dimension $72$
CM no
Inner twists $8$

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Show commands: Magma / PariGP / SageMath

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.

\(\operatorname{Tr}(f)(q) = \) \( 72 q - 32 q^{4}+O(q^{10}) \) Copy content Toggle raw display
\(\operatorname{Tr}(f)(q) = \) \( 72 q - 32 q^{4} - 24 q^{16} + 48 q^{22} + 28 q^{25} + 120 q^{40} - 56 q^{43} - 20 q^{49} - 72 q^{52} + 24 q^{61} + 160 q^{64} - 28 q^{79} - 216 q^{82} - 96 q^{88} - 42 q^{91} - 216 q^{94}+O(q^{100}) \) 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   \( a_{2} \) \( a_{3} \) \( a_{4} \) \( a_{5} \) \( a_{6} \) \( a_{7} \) \( a_{8} \) \( a_{9} \) \( a_{10} \)
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
\(n\): e.g. 2-40 or 990-1000
Embeddings: e.g. 1-3 or 467.36
Significant digits:
Format:

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 \(S_{2}^{\mathrm{new}}(819, [\chi])\).