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Properties

Label 4020.2.q.m
Level $4020$
Weight $2$
Character orbit 4020.q
Analytic conductor $32.100$
Analytic rank $0$
Dimension $24$
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: \(24\)
Relative dimension: \(12\) 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.

\(\operatorname{Tr}(f)(q) = \) \( 24 q + 24 q^{3} + 24 q^{5} - 3 q^{7} + 24 q^{9}+O(q^{10}) \) Copy content Toggle raw display
\(\operatorname{Tr}(f)(q) = \) \( 24 q + 24 q^{3} + 24 q^{5} - 3 q^{7} + 24 q^{9} - 2 q^{13} + 24 q^{15} - 6 q^{19} - 3 q^{21} + 2 q^{23} + 24 q^{25} + 24 q^{27} + 7 q^{29} - 8 q^{31} - 3 q^{35} - 10 q^{37} - 2 q^{39} + 2 q^{41} + 28 q^{43} + 24 q^{45} - 3 q^{47} - 17 q^{49} + 36 q^{53} - 6 q^{57} - 10 q^{59} + 9 q^{61} - 3 q^{63} - 2 q^{65} - 46 q^{67} + 2 q^{69} - 12 q^{71} + 6 q^{73} + 24 q^{75} - 5 q^{77} + 2 q^{79} + 24 q^{81} + 11 q^{83} + 7 q^{87} + 52 q^{89} - 22 q^{91} - 8 q^{93} - 6 q^{95} + 3 q^{97}+O(q^{100}) \) 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 −2.18663 + 3.78736i 0 1.00000 0
841.2 0 1.00000 0 1.00000 0 −2.09133 + 3.62228i 0 1.00000 0
841.3 0 1.00000 0 1.00000 0 −1.96234 + 3.39887i 0 1.00000 0
841.4 0 1.00000 0 1.00000 0 −1.09486 + 1.89635i 0 1.00000 0
841.5 0 1.00000 0 1.00000 0 −0.436767 + 0.756503i 0 1.00000 0
841.6 0 1.00000 0 1.00000 0 −0.388910 + 0.673613i 0 1.00000 0
841.7 0 1.00000 0 1.00000 0 0.134465 − 0.232901i 0 1.00000 0
841.8 0 1.00000 0 1.00000 0 0.440752 − 0.763405i 0 1.00000 0
841.9 0 1.00000 0 1.00000 0 0.983461 − 1.70340i 0 1.00000 0
841.10 0 1.00000 0 1.00000 0 1.00432 − 1.73954i 0 1.00000 0
841.11 0 1.00000 0 1.00000 0 1.80478 − 3.12597i 0 1.00000 0
841.12 0 1.00000 0 1.00000 0 2.29305 − 3.97167i 0 1.00000 0
3781.1 0 1.00000 0 1.00000 0 −2.18663 − 3.78736i 0 1.00000 0
3781.2 0 1.00000 0 1.00000 0 −2.09133 − 3.62228i 0 1.00000 0
3781.3 0 1.00000 0 1.00000 0 −1.96234 − 3.39887i 0 1.00000 0
3781.4 0 1.00000 0 1.00000 0 −1.09486 − 1.89635i 0 1.00000 0
3781.5 0 1.00000 0 1.00000 0 −0.436767 − 0.756503i 0 1.00000 0
3781.6 0 1.00000 0 1.00000 0 −0.388910 − 0.673613i 0 1.00000 0
3781.7 0 1.00000 0 1.00000 0 0.134465 + 0.232901i 0 1.00000 0
3781.8 0 1.00000 0 1.00000 0 0.440752 + 0.763405i 0 1.00000 0
See all 24 embeddings
\(n\): e.g. 2-40 or 990-1000
Embeddings: e.g. 1-3 or 841.12
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.m ✓ 24
67.c even 3 1 inner 4020.2.q.m ✓ 24
    
        By twisted newform orbit
Twist Min Dim Char Parity Ord Mult Type
4020.2.q.m ✓ 24 1.a even 1 1 trivial
4020.2.q.m ✓ 24 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 \(S_{2}^{\mathrm{new}}(4020, [\chi])\):

\( T_{7}^{24} + 3 T_{7}^{23} + 55 T_{7}^{22} + 110 T_{7}^{21} + 1762 T_{7}^{20} + 2939 T_{7}^{19} + \cdots + 2742336 \) Copy content Toggle raw display
\( T_{11}^{24} + 86 T_{11}^{22} - 26 T_{11}^{21} + 4727 T_{11}^{20} - 1886 T_{11}^{19} + 155557 T_{11}^{18} + \cdots + 14482196964 \) Copy content Toggle raw display
\( T_{17}^{24} + 134 T_{17}^{22} - 224 T_{17}^{21} + 12038 T_{17}^{20} - 25475 T_{17}^{19} + \cdots + 253956096 \) Copy content Toggle raw display