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Properties

Label 2880.2.bl.c
Level $2880$
Weight $2$
Character orbit 2880.bl
Analytic conductor $22.997$
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] = [2880,2,Mod(431,2880)]
 
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([2, 3, 2, 0]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("2880.431");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 2880 = 2^{6} \cdot 3^{2} \cdot 5 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 2880.bl (of order \(4\), degree \(2\), not 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: no (minimal twist has level 720)
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
\(\operatorname{Tr}(f)(q) = \) \( 32 q + 8 q^{19} - 32 q^{49} + 16 q^{55} + 16 q^{61} - 16 q^{67} + 16 q^{85} + 16 q^{91}+O(q^{100}) \) 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   \( a_{2} \) \( a_{3} \) \( a_{4} \) \( a_{5} \) \( a_{6} \) \( a_{7} \) \( a_{8} \) \( a_{9} \) \( a_{10} \)
431.1 0 0 0 −0.707107 − 0.707107i 0 3.01345 0 0 0
431.2 0 0 0 −0.707107 − 0.707107i 0 −3.83891 0 0 0
431.3 0 0 0 −0.707107 − 0.707107i 0 −0.841567 0 0 0
431.4 0 0 0 −0.707107 − 0.707107i 0 −2.45331 0 0 0
431.5 0 0 0 −0.707107 − 0.707107i 0 1.80170 0 0 0
431.6 0 0 0 −0.707107 − 0.707107i 0 −1.44621 0 0 0
431.7 0 0 0 −0.707107 − 0.707107i 0 3.46834 0 0 0
431.8 0 0 0 −0.707107 − 0.707107i 0 0.296505 0 0 0
431.9 0 0 0 0.707107 + 0.707107i 0 3.46834 0 0 0
431.10 0 0 0 0.707107 + 0.707107i 0 −0.841567 0 0 0
431.11 0 0 0 0.707107 + 0.707107i 0 −3.83891 0 0 0
431.12 0 0 0 0.707107 + 0.707107i 0 −1.44621 0 0 0
431.13 0 0 0 0.707107 + 0.707107i 0 3.01345 0 0 0
431.14 0 0 0 0.707107 + 0.707107i 0 1.80170 0 0 0
431.15 0 0 0 0.707107 + 0.707107i 0 −2.45331 0 0 0
431.16 0 0 0 0.707107 + 0.707107i 0 0.296505 0 0 0
1871.1 0 0 0 −0.707107 + 0.707107i 0 3.01345 0 0 0
1871.2 0 0 0 −0.707107 + 0.707107i 0 −3.83891 0 0 0
1871.3 0 0 0 −0.707107 + 0.707107i 0 −0.841567 0 0 0
1871.4 0 0 0 −0.707107 + 0.707107i 0 −2.45331 0 0 0
See all 32 embeddings
\(n\): e.g. 2-40 or 990-1000
Embeddings: e.g. 1-3 or 431.16
Significant digits:
Format:

Inner twists

Char Parity Ord Mult Type
1.a even 1 1 trivial
3.b odd 2 1 inner
16.f odd 4 1 inner
48.k 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.bl.c 32
3.b odd 2 1 inner 2880.2.bl.c 32
4.b odd 2 1 720.2.bl.c ✓ 32
12.b even 2 1 720.2.bl.c ✓ 32
16.e even 4 1 720.2.bl.c ✓ 32
16.f odd 4 1 inner 2880.2.bl.c 32
48.i odd 4 1 720.2.bl.c ✓ 32
48.k even 4 1 inner 2880.2.bl.c 32
    
        By twisted newform orbit
Twist Min Dim Char Parity Ord Mult Type
720.2.bl.c ✓ 32 4.b odd 2 1
720.2.bl.c ✓ 32 12.b even 2 1
720.2.bl.c ✓ 32 16.e even 4 1
720.2.bl.c ✓ 32 48.i odd 4 1
2880.2.bl.c 32 1.a even 1 1 trivial
2880.2.bl.c 32 3.b odd 2 1 inner
2880.2.bl.c 32 16.f odd 4 1 inner
2880.2.bl.c 32 48.k even 4 1 inner

Hecke kernels

This newform subspace can be constructed as the kernel of the linear operator \( T_{7}^{8} - 24T_{7}^{6} + 164T_{7}^{4} + 32T_{7}^{3} - 320T_{7}^{2} - 128T_{7} + 64 \) acting on \(S_{2}^{\mathrm{new}}(2880, [\chi])\). Copy content Toggle raw display