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Properties

Label 1014.3.f.l
Level $1014$
Weight $3$
Character orbit 1014.f
Analytic conductor $27.629$
Analytic rank $0$
Dimension $24$
Inner twists $2$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [1014,3,Mod(577,1014)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(1014, base_ring=CyclotomicField(4))
 
chi = DirichletCharacter(H, H._module([0, 3]))
 
N = Newforms(chi, 3, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("1014.577");
 
S:= CuspForms(chi, 3);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 1014 = 2 \cdot 3 \cdot 13^{2} \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 1014.f (of order \(4\), 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: \(27.6294988061\)
Analytic rank: \(0\)
Dimension: \(24\)
Relative dimension: \(12\) over \(\Q(i)\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{4}]$

$q$-expansion

The algebraic \(q\)-expansion of this newform has not been computed, but we have computed the trace expansion.

\(\operatorname{Tr}(f)(q) = \) \( 24 q + 24 q^{2} + 8 q^{5} + 24 q^{7} - 48 q^{8} + 72 q^{9} + 64 q^{11} + 48 q^{14} + 24 q^{15} - 96 q^{16} + 72 q^{18} + 160 q^{19} - 16 q^{20} + 128 q^{22} + 48 q^{28} + 8 q^{29} - 176 q^{31} - 96 q^{32}+ \cdots + 192 q^{99}+O(q^{100}) \) Copy content Toggle raw display

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   \( a_{2} \) \( a_{3} \) \( a_{4} \) \( a_{5} \) \( a_{6} \) \( a_{7} \) \( a_{8} \) \( a_{9} \) \( a_{10} \)
577.1 1.00000 − 1.00000i −1.73205 − 2.00000i 6.13024 − 6.13024i −1.73205 + 1.73205i −7.22737 − 7.22737i −2.00000 − 2.00000i 3.00000 − 12.2605i
577.2 1.00000 − 1.00000i −1.73205 − 2.00000i 1.79330 − 1.79330i −1.73205 + 1.73205i −1.33439 − 1.33439i −2.00000 − 2.00000i 3.00000 − 3.58660i
577.3 1.00000 − 1.00000i −1.73205 − 2.00000i −2.55415 + 2.55415i −1.73205 + 1.73205i 5.86894 + 5.86894i −2.00000 − 2.00000i 3.00000 5.10829i
577.4 1.00000 − 1.00000i −1.73205 − 2.00000i −1.48148 + 1.48148i −1.73205 + 1.73205i 1.99239 + 1.99239i −2.00000 − 2.00000i 3.00000 2.96297i
577.5 1.00000 − 1.00000i −1.73205 − 2.00000i 0.325674 − 0.325674i −1.73205 + 1.73205i −1.39966 − 1.39966i −2.00000 − 2.00000i 3.00000 − 0.651349i
577.6 1.00000 − 1.00000i −1.73205 − 2.00000i −5.67769 + 5.67769i −1.73205 + 1.73205i 8.10009 + 8.10009i −2.00000 − 2.00000i 3.00000 11.3554i
577.7 1.00000 − 1.00000i 1.73205 − 2.00000i 2.81770 − 2.81770i 1.73205 − 1.73205i 0.00760663 + 0.00760663i −2.00000 − 2.00000i 3.00000 − 5.63540i
577.8 1.00000 − 1.00000i 1.73205 − 2.00000i −0.400777 + 0.400777i 1.73205 − 1.73205i 9.22737 + 9.22737i −2.00000 − 2.00000i 3.00000 0.801554i
577.9 1.00000 − 1.00000i 1.73205 − 2.00000i −0.315011 + 0.315011i 1.73205 − 1.73205i 3.33439 + 3.33439i −2.00000 − 2.00000i 3.00000 0.630023i
577.10 1.00000 − 1.00000i 1.73205 − 2.00000i −3.76999 + 3.76999i 1.73205 − 1.73205i −3.86894 − 3.86894i −2.00000 − 2.00000i 3.00000 7.53998i
577.11 1.00000 − 1.00000i 1.73205 − 2.00000i 1.79162 − 1.79162i 1.73205 − 1.73205i −6.10009 − 6.10009i −2.00000 − 2.00000i 3.00000 − 3.58324i
577.12 1.00000 − 1.00000i 1.73205 − 2.00000i 5.34056 − 5.34056i 1.73205 − 1.73205i 3.39966 + 3.39966i −2.00000 − 2.00000i 3.00000 − 10.6811i
775.1 1.00000 + 1.00000i −1.73205 2.00000i 6.13024 + 6.13024i −1.73205 − 1.73205i −7.22737 + 7.22737i −2.00000 + 2.00000i 3.00000 12.2605i
775.2 1.00000 + 1.00000i −1.73205 2.00000i 1.79330 + 1.79330i −1.73205 − 1.73205i −1.33439 + 1.33439i −2.00000 + 2.00000i 3.00000 3.58660i
775.3 1.00000 + 1.00000i −1.73205 2.00000i −2.55415 − 2.55415i −1.73205 − 1.73205i 5.86894 − 5.86894i −2.00000 + 2.00000i 3.00000 − 5.10829i
775.4 1.00000 + 1.00000i −1.73205 2.00000i −1.48148 − 1.48148i −1.73205 − 1.73205i 1.99239 − 1.99239i −2.00000 + 2.00000i 3.00000 − 2.96297i
775.5 1.00000 + 1.00000i −1.73205 2.00000i 0.325674 + 0.325674i −1.73205 − 1.73205i −1.39966 + 1.39966i −2.00000 + 2.00000i 3.00000 0.651349i
775.6 1.00000 + 1.00000i −1.73205 2.00000i −5.67769 − 5.67769i −1.73205 − 1.73205i 8.10009 − 8.10009i −2.00000 + 2.00000i 3.00000 − 11.3554i
775.7 1.00000 + 1.00000i 1.73205 2.00000i 2.81770 + 2.81770i 1.73205 + 1.73205i 0.00760663 − 0.00760663i −2.00000 + 2.00000i 3.00000 5.63540i
775.8 1.00000 + 1.00000i 1.73205 2.00000i −0.400777 − 0.400777i 1.73205 + 1.73205i 9.22737 − 9.22737i −2.00000 + 2.00000i 3.00000 − 0.801554i
See all 24 embeddings
\(n\): e.g. 2-40 or 990-1000
Embeddings: e.g. 1-3 or 577.12
Significant digits:
Format:

Inner twists

Char Parity Ord Mult Type
1.a even 1 1 trivial
13.d odd 4 1 inner

Twists

       By twisting character orbit
Char Parity Ord Mult Type Twist Min Dim
1.a even 1 1 trivial 1014.3.f.l yes 24
13.b even 2 1 1014.3.f.k ✓ 24
13.d odd 4 1 1014.3.f.k ✓ 24
13.d odd 4 1 inner 1014.3.f.l yes 24
    
        By twisted newform orbit
Twist Min Dim Char Parity Ord Mult Type
1014.3.f.k ✓ 24 13.b even 2 1
1014.3.f.k ✓ 24 13.d odd 4 1
1014.3.f.l yes 24 1.a even 1 1 trivial
1014.3.f.l yes 24 13.d odd 4 1 inner

Hecke kernels

This newform subspace can be constructed as the intersection of the kernels of the following linear operators acting on \(S_{3}^{\mathrm{new}}(1014, [\chi])\):

\( T_{5}^{24} - 8 T_{5}^{23} + 32 T_{5}^{22} + 128 T_{5}^{21} + 5660 T_{5}^{20} - 40712 T_{5}^{19} + \cdots + 3990322561 \) Copy content Toggle raw display
\( T_{7}^{24} - 24 T_{7}^{23} + 288 T_{7}^{22} - 1056 T_{7}^{21} + 18588 T_{7}^{20} - 411184 T_{7}^{19} + \cdots + 2360915221729 \) Copy content Toggle raw display