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Properties

Label 4020.2.q.l
Level $4020$
Weight $2$
Character orbit 4020.q
Analytic conductor $32.100$
Analytic rank $0$
Dimension $22$
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] = [4020,2,Mod(841,4020)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(4020, base_ring=CyclotomicField(6))
 
chi = DirichletCharacter(H, H._module([0, 0, 0, 2]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("4020.841");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 4020 = 2^{2} \cdot 3 \cdot 5 \cdot 67 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 4020.q (of order \(3\), 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: \(32.0998616126\)
Analytic rank: \(0\)
Dimension: \(22\)
Relative dimension: \(11\) over \(\Q(\zeta_{3})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

$q$-expansion

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

\(\operatorname{Tr}(f)(q) = \) \( 22 q - 22 q^{3} - 22 q^{5} + q^{7} + 22 q^{9}+O(q^{10}) \) Copy content Toggle raw display
\(\operatorname{Tr}(f)(q) = \) \( 22 q - 22 q^{3} - 22 q^{5} + q^{7} + 22 q^{9} - 6 q^{11} - 7 q^{13} + 22 q^{15} + 4 q^{17} + 2 q^{19} - q^{21} + 6 q^{23} + 22 q^{25} - 22 q^{27} + 15 q^{29} - 5 q^{31} + 6 q^{33} - q^{35} + 2 q^{37} + 7 q^{39} - 6 q^{43} - 22 q^{45} - 7 q^{47} - 16 q^{49} - 4 q^{51} + 8 q^{53} + 6 q^{55} - 2 q^{57} - 6 q^{59} + 8 q^{61} + q^{63} + 7 q^{65} - 9 q^{67} - 6 q^{69} + 12 q^{71} - q^{73} - 22 q^{75} + 9 q^{77} - 15 q^{79} + 22 q^{81} - q^{83} - 4 q^{85} - 15 q^{87} + 20 q^{89} + 18 q^{91} + 5 q^{93} - 2 q^{95} - 16 q^{97} - 6 q^{99}+O(q^{100}) \) 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   \( a_{2} \) \( a_{3} \) \( a_{4} \) \( a_{5} \) \( a_{6} \) \( a_{7} \) \( a_{8} \) \( a_{9} \) \( a_{10} \)
841.1 0 −1.00000 0 −1.00000 0 −2.18326 + 3.78152i 0 1.00000 0
841.2 0 −1.00000 0 −1.00000 0 −1.77038 + 3.06640i 0 1.00000 0
841.3 0 −1.00000 0 −1.00000 0 −1.49766 + 2.59403i 0 1.00000 0
841.4 0 −1.00000 0 −1.00000 0 −0.775137 + 1.34258i 0 1.00000 0
841.5 0 −1.00000 0 −1.00000 0 −0.533315 + 0.923729i 0 1.00000 0
841.6 0 −1.00000 0 −1.00000 0 0.278615 − 0.482575i 0 1.00000 0
841.7 0 −1.00000 0 −1.00000 0 0.479055 − 0.829747i 0 1.00000 0
841.8 0 −1.00000 0 −1.00000 0 0.637931 − 1.10493i 0 1.00000 0
841.9 0 −1.00000 0 −1.00000 0 1.82121 − 3.15443i 0 1.00000 0
841.10 0 −1.00000 0 −1.00000 0 1.92862 − 3.34047i 0 1.00000 0
841.11 0 −1.00000 0 −1.00000 0 2.11433 − 3.66213i 0 1.00000 0
3781.1 0 −1.00000 0 −1.00000 0 −2.18326 − 3.78152i 0 1.00000 0
3781.2 0 −1.00000 0 −1.00000 0 −1.77038 − 3.06640i 0 1.00000 0
3781.3 0 −1.00000 0 −1.00000 0 −1.49766 − 2.59403i 0 1.00000 0
3781.4 0 −1.00000 0 −1.00000 0 −0.775137 − 1.34258i 0 1.00000 0
3781.5 0 −1.00000 0 −1.00000 0 −0.533315 − 0.923729i 0 1.00000 0
3781.6 0 −1.00000 0 −1.00000 0 0.278615 + 0.482575i 0 1.00000 0
3781.7 0 −1.00000 0 −1.00000 0 0.479055 + 0.829747i 0 1.00000 0
3781.8 0 −1.00000 0 −1.00000 0 0.637931 + 1.10493i 0 1.00000 0
3781.9 0 −1.00000 0 −1.00000 0 1.82121 + 3.15443i 0 1.00000 0
See all 22 embeddings
\(n\): e.g. 2-40 or 990-1000
Embeddings: e.g. 1-3 or 841.11
Significant digits:
Format:

Inner twists

Char Parity Ord Mult Type
1.a even 1 1 trivial
67.c even 3 1 inner

Twists

       By twisting character orbit
Char Parity Ord Mult Type Twist Min Dim
1.a even 1 1 trivial 4020.2.q.l ✓ 22
67.c even 3 1 inner 4020.2.q.l ✓ 22
    
        By twisted newform orbit
Twist Min Dim Char Parity Ord Mult Type
4020.2.q.l ✓ 22 1.a even 1 1 trivial
4020.2.q.l ✓ 22 67.c even 3 1 inner

Hecke kernels

This newform subspace can be constructed as the intersection of the kernels of the following linear operators acting on \(S_{2}^{\mathrm{new}}(4020, [\chi])\):

\( T_{7}^{22} - T_{7}^{21} + 47 T_{7}^{20} - 30 T_{7}^{19} + 1420 T_{7}^{18} - 729 T_{7}^{17} + \cdots + 9603801 \) Copy content Toggle raw display
\( T_{11}^{22} + 6 T_{11}^{21} + 74 T_{11}^{20} + 406 T_{11}^{19} + 3337 T_{11}^{18} + 16360 T_{11}^{17} + \cdots + 20729809 \) Copy content Toggle raw display
\( T_{17}^{22} - 4 T_{17}^{21} + 120 T_{17}^{20} - 476 T_{17}^{19} + 9450 T_{17}^{18} - 38405 T_{17}^{17} + \cdots + 6233260401 \) Copy content Toggle raw display