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Properties

Label 4020.3.c.a
Level $4020$
Weight $3$
Character orbit 4020.c
Analytic conductor $109.537$
Analytic rank $0$
Dimension $92$
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] = [4020,3,Mod(1741,4020)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(4020, base_ring=CyclotomicField(2))
 
chi = DirichletCharacter(H, H._module([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("4020.1741");
 
S:= CuspForms(chi, 3);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 4020 = 2^{2} \cdot 3 \cdot 5 \cdot 67 \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 4020.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: \(109.537066273\)
Analytic rank: \(0\)
Dimension: \(92\)
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.

\(\operatorname{Tr}(f)(q) = \) \( 92 q - 276 q^{9}+O(q^{10}) \) Copy content Toggle raw display
\(\operatorname{Tr}(f)(q) = \) \( 92 q - 276 q^{9} - 100 q^{17} - 44 q^{19} + 24 q^{21} + 36 q^{23} - 460 q^{25} + 108 q^{29} + 40 q^{35} + 68 q^{37} + 24 q^{39} + 36 q^{47} - 628 q^{49} - 120 q^{55} + 124 q^{59} + 40 q^{65} + 68 q^{67} - 48 q^{71} + 268 q^{73} - 80 q^{77} + 828 q^{81} - 232 q^{83} + 444 q^{89} - 248 q^{91} + 48 q^{93}+O(q^{100}) \) 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   \( a_{2} \) \( a_{3} \) \( a_{4} \) \( a_{5} \) \( a_{6} \) \( a_{7} \) \( a_{8} \) \( a_{9} \) \( a_{10} \)
1741.1 0 − 1.73205i 0 − 2.23607i 0 − 12.0600i 0 −3.00000 0
1741.2 0 − 1.73205i 0 − 2.23607i 0 − 11.8613i 0 −3.00000 0
1741.3 0 − 1.73205i 0 − 2.23607i 0 − 10.5071i 0 −3.00000 0
1741.4 0 − 1.73205i 0 − 2.23607i 0 − 8.59283i 0 −3.00000 0
1741.5 0 − 1.73205i 0 − 2.23607i 0 − 6.90907i 0 −3.00000 0
1741.6 0 − 1.73205i 0 − 2.23607i 0 − 5.16696i 0 −3.00000 0
1741.7 0 − 1.73205i 0 − 2.23607i 0 − 4.08895i 0 −3.00000 0
1741.8 0 − 1.73205i 0 − 2.23607i 0 − 2.85330i 0 −3.00000 0
1741.9 0 − 1.73205i 0 − 2.23607i 0 − 1.94478i 0 −3.00000 0
1741.10 0 − 1.73205i 0 − 2.23607i 0 − 1.52599i 0 −3.00000 0
1741.11 0 − 1.73205i 0 − 2.23607i 0 − 0.547779i 0 −3.00000 0
1741.12 0 − 1.73205i 0 − 2.23607i 0 − 0.0398799i 0 −3.00000 0
1741.13 0 − 1.73205i 0 − 2.23607i 0 0.0652957i 0 −3.00000 0
1741.14 0 − 1.73205i 0 − 2.23607i 0 1.10923i 0 −3.00000 0
1741.15 0 − 1.73205i 0 − 2.23607i 0 1.97365i 0 −3.00000 0
1741.16 0 − 1.73205i 0 − 2.23607i 0 5.11354i 0 −3.00000 0
1741.17 0 − 1.73205i 0 − 2.23607i 0 6.58558i 0 −3.00000 0
1741.18 0 − 1.73205i 0 − 2.23607i 0 7.15379i 0 −3.00000 0
1741.19 0 − 1.73205i 0 − 2.23607i 0 7.56225i 0 −3.00000 0
1741.20 0 − 1.73205i 0 − 2.23607i 0 8.64338i 0 −3.00000 0
See all 92 embeddings
\(n\): e.g. 2-40 or 990-1000
Embeddings: e.g. 1-3 or 1741.92
Significant digits:
Format:

Inner twists

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

Twists

       By twisting character orbit
Char Parity Ord Mult Type Twist Min Dim
1.a even 1 1 trivial 4020.3.c.a ✓ 92
67.b odd 2 1 inner 4020.3.c.a ✓ 92
    
        By twisted newform orbit
Twist Min Dim Char Parity Ord Mult Type
4020.3.c.a ✓ 92 1.a even 1 1 trivial
4020.3.c.a ✓ 92 67.b odd 2 1 inner

Hecke kernels

This newform subspace is the entire newspace \(S_{3}^{\mathrm{new}}(4020, [\chi])\).