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Properties

Label 4140.3.c.a
Level $4140$
Weight $3$
Character orbit 4140.c
Analytic conductor $112.807$
Analytic rank $0$
Dimension $88$
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] = [4140,3,Mod(4049,4140)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(4140, base_ring=CyclotomicField(2))
 
chi = DirichletCharacter(H, H._module([0, 1, 1, 0]))
 
N = Newforms(chi, 3, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("4140.4049");
 
S:= CuspForms(chi, 3);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 4140 = 2^{2} \cdot 3^{2} \cdot 5 \cdot 23 \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 4140.c (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: \(112.806829445\)
Analytic rank: \(0\)
Dimension: \(88\)
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.

\(\operatorname{Tr}(f)(q) = \) \( 88 q+O(q^{10}) \) Copy content Toggle raw display
\(\operatorname{Tr}(f)(q) = \) \( 88 q - 16 q^{19} - 48 q^{25} + 272 q^{31} - 600 q^{49} + 112 q^{55} + 448 q^{61} - 32 q^{79} - 264 q^{85} - 16 q^{91}+O(q^{100}) \) 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   \( a_{2} \) \( a_{3} \) \( a_{4} \) \( a_{5} \) \( a_{6} \) \( a_{7} \) \( a_{8} \) \( a_{9} \) \( a_{10} \)
4049.1 0 0 0 −4.99275 − 0.269219i 0 − 13.6272i 0 0 0
4049.2 0 0 0 −4.99275 + 0.269219i 0 13.6272i 0 0 0
4049.3 0 0 0 −4.95880 − 0.640555i 0 5.90914i 0 0 0
4049.4 0 0 0 −4.95880 + 0.640555i 0 − 5.90914i 0 0 0
4049.5 0 0 0 −4.81534 − 1.34629i 0 4.38152i 0 0 0
4049.6 0 0 0 −4.81534 + 1.34629i 0 − 4.38152i 0 0 0
4049.7 0 0 0 −4.79317 − 1.42321i 0 − 6.33514i 0 0 0
4049.8 0 0 0 −4.79317 + 1.42321i 0 6.33514i 0 0 0
4049.9 0 0 0 −4.77264 − 1.49061i 0 2.56481i 0 0 0
4049.10 0 0 0 −4.77264 + 1.49061i 0 − 2.56481i 0 0 0
4049.11 0 0 0 −4.60834 − 1.93989i 0 − 1.03288i 0 0 0
4049.12 0 0 0 −4.60834 + 1.93989i 0 1.03288i 0 0 0
4049.13 0 0 0 −4.49878 − 2.18197i 0 − 10.0913i 0 0 0
4049.14 0 0 0 −4.49878 + 2.18197i 0 10.0913i 0 0 0
4049.15 0 0 0 −4.41871 − 2.33986i 0 11.6062i 0 0 0
4049.16 0 0 0 −4.41871 + 2.33986i 0 − 11.6062i 0 0 0
4049.17 0 0 0 −3.90943 − 3.11711i 0 7.62373i 0 0 0
4049.18 0 0 0 −3.90943 + 3.11711i 0 − 7.62373i 0 0 0
4049.19 0 0 0 −3.78150 − 3.27113i 0 − 2.52965i 0 0 0
4049.20 0 0 0 −3.78150 + 3.27113i 0 2.52965i 0 0 0
See all 88 embeddings
\(n\): e.g. 2-40 or 990-1000
Embeddings: e.g. 1-3 or 4049.88
Significant digits:
Format:

Inner twists

Char Parity Ord Mult Type
1.a even 1 1 trivial
3.b odd 2 1 inner
5.b even 2 1 inner
15.d odd 2 1 inner

Twists

       By twisting character orbit
Char Parity Ord Mult Type Twist Min Dim
1.a even 1 1 trivial 4140.3.c.a ✓ 88
3.b odd 2 1 inner 4140.3.c.a ✓ 88
5.b even 2 1 inner 4140.3.c.a ✓ 88
15.d odd 2 1 inner 4140.3.c.a ✓ 88
    
        By twisted newform orbit
Twist Min Dim Char Parity Ord Mult Type
4140.3.c.a ✓ 88 1.a even 1 1 trivial
4140.3.c.a ✓ 88 3.b odd 2 1 inner
4140.3.c.a ✓ 88 5.b even 2 1 inner
4140.3.c.a ✓ 88 15.d odd 2 1 inner

Hecke kernels

This newform subspace is the entire newspace \(S_{3}^{\mathrm{new}}(4140, [\chi])\).