Properties

Label 2880.2.bj.f
Level $2880$
Weight $2$
Character orbit 2880.bj
Analytic conductor $22.997$
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] = [2880,2,Mod(737,2880)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(2880, base_ring=CyclotomicField(4))
 
chi = DirichletCharacter(H, H._module([0, 2, 2, 1]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("2880.737");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 2880 = 2^{6} \cdot 3^{2} \cdot 5 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 2880.bj (of order \(4\), 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: \(22.9969157821\)
Analytic rank: \(0\)
Dimension: \(32\)
Relative dimension: \(16\) over \(\Q(i)\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{4}]$

$q$-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
\(\operatorname{Tr}(f)(q) = \) \( 32 q + 32 q^{19} - 32 q^{43} + 96 q^{67} + 48 q^{73} + 144 q^{97}+O(q^{100}) \) 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   \( a_{2} \) \( a_{3} \) \( a_{4} \) \( a_{5} \) \( a_{6} \) \( a_{7} \) \( a_{8} \) \( a_{9} \) \( a_{10} \)
737.1 0 0 0 −2.11477 + 0.726469i 0 −3.61002 3.61002i 0 0 0
737.2 0 0 0 −2.11477 + 0.726469i 0 3.61002 + 3.61002i 0 0 0
737.3 0 0 0 −1.94535 1.10255i 0 −0.880206 0.880206i 0 0 0
737.4 0 0 0 −1.94535 1.10255i 0 0.880206 + 0.880206i 0 0 0
737.5 0 0 0 −1.27770 + 1.83507i 0 −0.254252 0.254252i 0 0 0
737.6 0 0 0 −1.27770 + 1.83507i 0 0.254252 + 0.254252i 0 0 0
737.7 0 0 0 −0.332926 2.21114i 0 −2.47556 2.47556i 0 0 0
737.8 0 0 0 −0.332926 2.21114i 0 2.47556 + 2.47556i 0 0 0
737.9 0 0 0 0.332926 + 2.21114i 0 −2.47556 2.47556i 0 0 0
737.10 0 0 0 0.332926 + 2.21114i 0 2.47556 + 2.47556i 0 0 0
737.11 0 0 0 1.27770 1.83507i 0 −0.254252 0.254252i 0 0 0
737.12 0 0 0 1.27770 1.83507i 0 0.254252 + 0.254252i 0 0 0
737.13 0 0 0 1.94535 + 1.10255i 0 −0.880206 0.880206i 0 0 0
737.14 0 0 0 1.94535 + 1.10255i 0 0.880206 + 0.880206i 0 0 0
737.15 0 0 0 2.11477 0.726469i 0 −3.61002 3.61002i 0 0 0
737.16 0 0 0 2.11477 0.726469i 0 3.61002 + 3.61002i 0 0 0
1313.1 0 0 0 −2.11477 0.726469i 0 −3.61002 + 3.61002i 0 0 0
1313.2 0 0 0 −2.11477 0.726469i 0 3.61002 3.61002i 0 0 0
1313.3 0 0 0 −1.94535 + 1.10255i 0 −0.880206 + 0.880206i 0 0 0
1313.4 0 0 0 −1.94535 + 1.10255i 0 0.880206 0.880206i 0 0 0
See all 32 embeddings
\(n\): e.g. 2-40 or 990-1000
Embeddings: e.g. 1-3 or 737.16
Significant digits:
Format:

Inner twists

Char Parity Ord Mult Type
1.a even 1 1 trivial
3.b odd 2 1 inner
8.d odd 2 1 inner
20.e even 4 1 inner
24.f even 2 1 inner
40.i odd 4 1 inner
60.l odd 4 1 inner
120.w even 4 1 inner

Twists

       By twisting character orbit
Char Parity Ord Mult Type Twist Min Dim
1.a even 1 1 trivial 2880.2.bj.f yes 32
3.b odd 2 1 inner 2880.2.bj.f yes 32
4.b odd 2 1 2880.2.bj.e 32
5.c odd 4 1 2880.2.bj.e 32
8.b even 2 1 2880.2.bj.e 32
8.d odd 2 1 inner 2880.2.bj.f yes 32
12.b even 2 1 2880.2.bj.e 32
15.e even 4 1 2880.2.bj.e 32
20.e even 4 1 inner 2880.2.bj.f yes 32
24.f even 2 1 inner 2880.2.bj.f yes 32
24.h odd 2 1 2880.2.bj.e 32
40.i odd 4 1 inner 2880.2.bj.f yes 32
40.k even 4 1 2880.2.bj.e 32
60.l odd 4 1 inner 2880.2.bj.f yes 32
120.q odd 4 1 2880.2.bj.e 32
120.w even 4 1 inner 2880.2.bj.f yes 32
    
        By twisted newform orbit
Twist Min Dim Char Parity Ord Mult Type
2880.2.bj.e 32 4.b odd 2 1
2880.2.bj.e 32 5.c odd 4 1
2880.2.bj.e 32 8.b even 2 1
2880.2.bj.e 32 12.b even 2 1
2880.2.bj.e 32 15.e even 4 1
2880.2.bj.e 32 24.h odd 2 1
2880.2.bj.e 32 40.k even 4 1
2880.2.bj.e 32 120.q odd 4 1
2880.2.bj.f yes 32 1.a even 1 1 trivial
2880.2.bj.f yes 32 3.b odd 2 1 inner
2880.2.bj.f yes 32 8.d odd 2 1 inner
2880.2.bj.f yes 32 20.e even 4 1 inner
2880.2.bj.f yes 32 24.f even 2 1 inner
2880.2.bj.f yes 32 40.i odd 4 1 inner
2880.2.bj.f yes 32 60.l odd 4 1 inner
2880.2.bj.f yes 32 120.w even 4 1 inner

Hecke kernels

This newform subspace can be constructed as the intersection of the kernels of the following linear operators acting on \(S_{2}^{\mathrm{new}}(2880, [\chi])\):

\( T_{7}^{16} + 832T_{7}^{12} + 104064T_{7}^{8} + 246784T_{7}^{4} + 4096 \) Copy content Toggle raw display
\( T_{19}^{4} - 4T_{19}^{3} - 24T_{19}^{2} + 80T_{19} - 32 \) Copy content Toggle raw display
\( T_{23}^{16} + 2560T_{23}^{12} + 1400832T_{23}^{8} + 189792256T_{23}^{4} + 16777216 \) Copy content Toggle raw display