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Properties

Label 1584.2.cb.a
Level $1584$
Weight $2$
Character orbit 1584.cb
Analytic conductor $12.648$
Analytic rank $0$
Dimension $32$
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] = [1584,2,Mod(575,1584)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(1584, base_ring=CyclotomicField(10))
 
chi = DirichletCharacter(H, H._module([5, 0, 5, 8]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("1584.575");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 1584 = 2^{4} \cdot 3^{2} \cdot 11 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1584.cb (of order \(10\), degree \(4\), 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: \(12.6483036802\)
Analytic rank: \(0\)
Dimension: \(32\)
Relative dimension: \(8\) over \(\Q(\zeta_{10})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{10}]$

$q$-expansion

The dimension is sufficiently large that we do not compute an algebraic \(q\)-expansion, but we have computed the trace expansion.

\(\operatorname{Tr}(f)(q) = \) \( 32 q+O(q^{10}) \) Copy content Toggle raw display
\(\operatorname{Tr}(f)(q) = \) \( 32 q - 16 q^{13} - 24 q^{37} - 64 q^{49} - 32 q^{61} - 8 q^{73} + 56 q^{85} + 40 q^{97}+O(q^{100}) \) Copy content Toggle raw display

Display 100 coefficients 10 coefficients

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   \( a_{2} \) \( a_{3} \) \( a_{4} \) \( a_{5} \) \( a_{6} \) \( a_{7} \) \( a_{8} \) \( a_{9} \) \( a_{10} \)
575.1 0 0 0 −1.54585 + 2.12768i 0 −2.75006 − 0.893550i 0 0 0
575.2 0 0 0 −1.54585 + 2.12768i 0 2.75006 + 0.893550i 0 0 0
575.3 0 0 0 −1.03211 + 1.42058i 0 0.792551 + 0.257516i 0 0 0
575.4 0 0 0 −1.03211 + 1.42058i 0 −0.792551 − 0.257516i 0 0 0
575.5 0 0 0 1.03211 − 1.42058i 0 0.792551 + 0.257516i 0 0 0
575.6 0 0 0 1.03211 − 1.42058i 0 −0.792551 − 0.257516i 0 0 0
575.7 0 0 0 1.54585 − 2.12768i 0 −2.75006 − 0.893550i 0 0 0
575.8 0 0 0 1.54585 − 2.12768i 0 2.75006 + 0.893550i 0 0 0
719.1 0 0 0 −1.54585 − 2.12768i 0 −2.75006 + 0.893550i 0 0 0
719.2 0 0 0 −1.54585 − 2.12768i 0 2.75006 − 0.893550i 0 0 0
719.3 0 0 0 −1.03211 − 1.42058i 0 −0.792551 + 0.257516i 0 0 0
719.4 0 0 0 −1.03211 − 1.42058i 0 0.792551 − 0.257516i 0 0 0
719.5 0 0 0 1.03211 + 1.42058i 0 −0.792551 + 0.257516i 0 0 0
719.6 0 0 0 1.03211 + 1.42058i 0 0.792551 − 0.257516i 0 0 0
719.7 0 0 0 1.54585 + 2.12768i 0 −2.75006 + 0.893550i 0 0 0
719.8 0 0 0 1.54585 + 2.12768i 0 2.75006 − 0.893550i 0 0 0
863.1 0 0 0 −2.91529 − 0.947235i 0 2.77348 + 3.81737i 0 0 0
863.2 0 0 0 −2.91529 − 0.947235i 0 −2.77348 − 3.81737i 0 0 0
863.3 0 0 0 −0.739038 − 0.240128i 0 1.27155 + 1.75014i 0 0 0
863.4 0 0 0 −0.739038 − 0.240128i 0 −1.27155 − 1.75014i 0 0 0
See all 32 embeddings
\(n\): e.g. 2-40 or 990-1000
Embeddings: e.g. 1-3 or 575.8
Significant digits:
Format:

Inner twists

Char Parity Ord Mult Type
1.a even 1 1 trivial
3.b odd 2 1 inner
4.b odd 2 1 inner
11.c even 5 1 inner
12.b even 2 1 inner
33.h odd 10 1 inner
44.h odd 10 1 inner
132.o even 10 1 inner

Twists

       By twisting character orbit
Char Parity Ord Mult Type Twist Min Dim
1.a even 1 1 trivial 1584.2.cb.a ✓ 32
3.b odd 2 1 inner 1584.2.cb.a ✓ 32
4.b odd 2 1 inner 1584.2.cb.a ✓ 32
11.c even 5 1 inner 1584.2.cb.a ✓ 32
12.b even 2 1 inner 1584.2.cb.a ✓ 32
33.h odd 10 1 inner 1584.2.cb.a ✓ 32
44.h odd 10 1 inner 1584.2.cb.a ✓ 32
132.o even 10 1 inner 1584.2.cb.a ✓ 32
    
        By twisted newform orbit
Twist Min Dim Char Parity Ord Mult Type
1584.2.cb.a ✓ 32 1.a even 1 1 trivial
1584.2.cb.a ✓ 32 3.b odd 2 1 inner
1584.2.cb.a ✓ 32 4.b odd 2 1 inner
1584.2.cb.a ✓ 32 11.c even 5 1 inner
1584.2.cb.a ✓ 32 12.b even 2 1 inner
1584.2.cb.a ✓ 32 33.h odd 10 1 inner
1584.2.cb.a ✓ 32 44.h odd 10 1 inner
1584.2.cb.a ✓ 32 132.o even 10 1 inner