Properties

Label 1456.2.cp.c
Level $1456$
Weight $2$
Character orbit 1456.cp
Analytic conductor $11.626$
Analytic rank $0$
Dimension $32$
CM no
Inner twists $4$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [1456,2,Mod(495,1456)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(1456, base_ring=CyclotomicField(6))
 
chi = DirichletCharacter(H, H._module([3, 0, 5, 0]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("1456.495");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 1456 = 2^{4} \cdot 7 \cdot 13 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1456.cp (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: \(11.6262185343\)
Analytic rank: \(0\)
Dimension: \(32\)
Relative dimension: \(16\) 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.

\(\operatorname{Tr}(f)(q) = \) \( 32 q + 12 q^{5} - 16 q^{9}+O(q^{10}) \) Copy content Toggle raw display
\(\operatorname{Tr}(f)(q) = \) \( 32 q + 12 q^{5} - 16 q^{9} - 36 q^{17} - 44 q^{21} + 32 q^{25} + 8 q^{29} + 24 q^{33} - 48 q^{45} - 28 q^{49} + 16 q^{57} - 24 q^{61} - 4 q^{65} + 60 q^{73} + 20 q^{77} - 40 q^{81} + 104 q^{85} - 12 q^{93}+O(q^{100}) \) 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   \( a_{2} \) \( a_{3} \) \( a_{4} \) \( a_{5} \) \( a_{6} \) \( a_{7} \) \( a_{8} \) \( a_{9} \) \( a_{10} \)
495.1 0 −1.68604 2.92030i 0 3.35997 + 1.93988i 0 2.60194 0.479515i 0 −4.18545 + 7.24942i 0
495.2 0 −1.36228 2.35953i 0 −2.81406 1.62470i 0 1.05058 2.42822i 0 −2.21160 + 3.83060i 0
495.3 0 −1.14890 1.98995i 0 −1.39339 0.804472i 0 1.87264 + 1.86901i 0 −1.13993 + 1.97442i 0
495.4 0 −1.01129 1.75161i 0 0.650003 + 0.375279i 0 −0.669765 + 2.55957i 0 −0.545433 + 0.944717i 0
495.5 0 −0.696784 1.20687i 0 1.38995 + 0.802488i 0 0.300336 2.62865i 0 0.528984 0.916227i 0
495.6 0 −0.669244 1.15916i 0 3.22760 + 1.86346i 0 −2.10372 1.60448i 0 0.604224 1.04655i 0
495.7 0 −0.120774 0.209186i 0 −2.59019 1.49545i 0 1.09375 2.40909i 0 1.47083 2.54755i 0
495.8 0 −0.103962 0.180067i 0 1.17011 + 0.675562i 0 2.63794 0.203192i 0 1.47838 2.56064i 0
495.9 0 0.103962 + 0.180067i 0 1.17011 + 0.675562i 0 −2.63794 + 0.203192i 0 1.47838 2.56064i 0
495.10 0 0.120774 + 0.209186i 0 −2.59019 1.49545i 0 −1.09375 + 2.40909i 0 1.47083 2.54755i 0
495.11 0 0.669244 + 1.15916i 0 3.22760 + 1.86346i 0 2.10372 + 1.60448i 0 0.604224 1.04655i 0
495.12 0 0.696784 + 1.20687i 0 1.38995 + 0.802488i 0 −0.300336 + 2.62865i 0 0.528984 0.916227i 0
495.13 0 1.01129 + 1.75161i 0 0.650003 + 0.375279i 0 0.669765 2.55957i 0 −0.545433 + 0.944717i 0
495.14 0 1.14890 + 1.98995i 0 −1.39339 0.804472i 0 −1.87264 1.86901i 0 −1.13993 + 1.97442i 0
495.15 0 1.36228 + 2.35953i 0 −2.81406 1.62470i 0 −1.05058 + 2.42822i 0 −2.21160 + 3.83060i 0
495.16 0 1.68604 + 2.92030i 0 3.35997 + 1.93988i 0 −2.60194 + 0.479515i 0 −4.18545 + 7.24942i 0
703.1 0 −1.68604 + 2.92030i 0 3.35997 1.93988i 0 2.60194 + 0.479515i 0 −4.18545 7.24942i 0
703.2 0 −1.36228 + 2.35953i 0 −2.81406 + 1.62470i 0 1.05058 + 2.42822i 0 −2.21160 3.83060i 0
703.3 0 −1.14890 + 1.98995i 0 −1.39339 + 0.804472i 0 1.87264 1.86901i 0 −1.13993 1.97442i 0
703.4 0 −1.01129 + 1.75161i 0 0.650003 0.375279i 0 −0.669765 2.55957i 0 −0.545433 0.944717i 0
See all 32 embeddings
\(n\): e.g. 2-40 or 990-1000
Embeddings: e.g. 1-3 or 495.16
Significant digits:
Format:

Inner twists

Char Parity Ord Mult Type
1.a even 1 1 trivial
4.b odd 2 1 inner
7.d odd 6 1 inner
28.f even 6 1 inner

Twists

       By twisting character orbit
Char Parity Ord Mult Type Twist Min Dim
1.a even 1 1 trivial 1456.2.cp.c 32
4.b odd 2 1 inner 1456.2.cp.c 32
7.d odd 6 1 inner 1456.2.cp.c 32
28.f even 6 1 inner 1456.2.cp.c 32
    
        By twisted newform orbit
Twist Min Dim Char Parity Ord Mult Type
1456.2.cp.c 32 1.a even 1 1 trivial
1456.2.cp.c 32 4.b odd 2 1 inner
1456.2.cp.c 32 7.d odd 6 1 inner
1456.2.cp.c 32 28.f even 6 1 inner