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Properties

Label 2760.3.g.a
Level $2760$
Weight $3$
Character orbit 2760.g
Analytic conductor $75.205$
Analytic rank $0$
Dimension $96$
CM no
Inner twists $2$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [2760,3,Mod(2161,2760)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(2760, base_ring=CyclotomicField(2))
 
chi = DirichletCharacter(H, H._module([0, 0, 0, 0, 1]))
 
N = Newforms(chi, 3, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("2760.2161");
 
S:= CuspForms(chi, 3);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 2760 = 2^{3} \cdot 3 \cdot 5 \cdot 23 \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 2760.g (of order \(2\), degree \(1\), 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: \(75.2045529634\)
Analytic rank: \(0\)
Dimension: \(96\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

$q$-expansion

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

\(\operatorname{Tr}(f)(q) = \) \( 96 q + 288 q^{9}+O(q^{10}) \) Copy content Toggle raw display
\(\operatorname{Tr}(f)(q) = \) \( 96 q + 288 q^{9} - 16 q^{23} - 480 q^{25} - 80 q^{31} + 80 q^{35} + 48 q^{39} + 112 q^{41} + 32 q^{47} - 688 q^{49} - 80 q^{55} - 496 q^{59} - 96 q^{69} - 416 q^{71} - 320 q^{73} + 864 q^{81} + 192 q^{93}+O(q^{100}) \) 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   \( a_{2} \) \( a_{3} \) \( a_{4} \) \( a_{5} \) \( a_{6} \) \( a_{7} \) \( a_{8} \) \( a_{9} \) \( a_{10} \)
2161.1 0 −1.73205 0 − 2.23607i 0 − 12.2824i 0 3.00000 0
2161.2 0 −1.73205 0 − 2.23607i 0 − 10.7897i 0 3.00000 0
2161.3 0 −1.73205 0 − 2.23607i 0 − 10.5413i 0 3.00000 0
2161.4 0 −1.73205 0 − 2.23607i 0 − 7.16885i 0 3.00000 0
2161.5 0 −1.73205 0 − 2.23607i 0 − 7.15300i 0 3.00000 0
2161.6 0 −1.73205 0 − 2.23607i 0 − 6.71584i 0 3.00000 0
2161.7 0 −1.73205 0 − 2.23607i 0 − 5.50203i 0 3.00000 0
2161.8 0 −1.73205 0 − 2.23607i 0 − 5.01595i 0 3.00000 0
2161.9 0 −1.73205 0 − 2.23607i 0 − 4.66176i 0 3.00000 0
2161.10 0 −1.73205 0 − 2.23607i 0 − 2.69051i 0 3.00000 0
2161.11 0 −1.73205 0 − 2.23607i 0 − 1.58351i 0 3.00000 0
2161.12 0 −1.73205 0 − 2.23607i 0 0.00406525i 0 3.00000 0
2161.13 0 −1.73205 0 − 2.23607i 0 1.24234i 0 3.00000 0
2161.14 0 −1.73205 0 − 2.23607i 0 3.56454i 0 3.00000 0
2161.15 0 −1.73205 0 − 2.23607i 0 4.06988i 0 3.00000 0
2161.16 0 −1.73205 0 − 2.23607i 0 4.35205i 0 3.00000 0
2161.17 0 −1.73205 0 − 2.23607i 0 5.23512i 0 3.00000 0
2161.18 0 −1.73205 0 − 2.23607i 0 5.37611i 0 3.00000 0
2161.19 0 −1.73205 0 − 2.23607i 0 6.39488i 0 3.00000 0
2161.20 0 −1.73205 0 − 2.23607i 0 7.31842i 0 3.00000 0
See all 96 embeddings
\(n\): e.g. 2-40 or 990-1000
Embeddings: e.g. 1-3 or 2161.96
Significant digits:
Format:

Inner twists

Char Parity Ord Mult Type
1.a even 1 1 trivial
23.b odd 2 1 inner

Twists

       By twisting character orbit
Char Parity Ord Mult Type Twist Min Dim
1.a even 1 1 trivial 2760.3.g.a ✓ 96
23.b odd 2 1 inner 2760.3.g.a ✓ 96
    
        By twisted newform orbit
Twist Min Dim Char Parity Ord Mult Type
2760.3.g.a ✓ 96 1.a even 1 1 trivial
2760.3.g.a ✓ 96 23.b odd 2 1 inner

Hecke kernels

This newform subspace is the entire newspace \(S_{3}^{\mathrm{new}}(2760, [\chi])\).