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Properties

Label 8967.2.a.bl
Level $8967$
Weight $2$
Character orbit 8967.a
Self dual yes
Analytic conductor $71.602$
Analytic rank $0$
Dimension $21$
CM no
Inner twists $1$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [8967,2,Mod(1,8967)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(8967, base_ring=CyclotomicField(2))
 
chi = DirichletCharacter(H, H._module([0, 0, 0]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("8967.1");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 8967 = 3 \cdot 7^{2} \cdot 61 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 8967.a (trivial)

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: yes
Analytic conductor: \(71.6018554925\)
Analytic rank: \(0\)
Dimension: \(21\)
Twist minimal: no (minimal twist has level 1281)
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

$q$-expansion

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

\(\operatorname{Tr}(f)(q) = \) \( 21 q + 21 q^{3} + 32 q^{4} + 11 q^{5} + 21 q^{9} + 6 q^{10} + q^{11} + 32 q^{12} + 14 q^{13} + 11 q^{15} + 30 q^{16} + 21 q^{17} + 4 q^{19} + 26 q^{20} + 4 q^{22} + 8 q^{23} + 20 q^{25} + 38 q^{26} + 21 q^{27}+ \cdots + q^{99}+O(q^{100}) \) 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   \( a_{2} \) \( a_{3} \) \( a_{4} \) \( a_{5} \) \( a_{6} \) \( a_{7} \) \( a_{8} \) \( a_{9} \) \( a_{10} \)
1.1 −2.79851 1.00000 5.83165 2.69028 −2.79851 0 −10.7229 1.00000 −7.52877
1.2 −2.74356 1.00000 5.52709 −1.80479 −2.74356 0 −9.67678 1.00000 4.95155
1.3 −2.36392 1.00000 3.58813 −1.69694 −2.36392 0 −3.75421 1.00000 4.01145
1.4 −2.09101 1.00000 2.37233 3.54651 −2.09101 0 −0.778540 1.00000 −7.41578
1.5 −1.83068 1.00000 1.35137 0.591980 −1.83068 0 1.18743 1.00000 −1.08372
1.6 −1.64447 1.00000 0.704275 1.69807 −1.64447 0 2.13078 1.00000 −2.79242
1.7 −1.50469 1.00000 0.264087 −2.27929 −1.50469 0 2.61201 1.00000 3.42961
1.8 −1.38113 1.00000 −0.0924791 0.506847 −1.38113 0 2.88999 1.00000 −0.700021
1.9 −0.950148 1.00000 −1.09722 −2.36436 −0.950148 0 2.94282 1.00000 2.24649
1.10 −0.647075 1.00000 −1.58129 4.33702 −0.647075 0 2.31737 1.00000 −2.80637
1.11 −0.0905074 1.00000 −1.99181 0.455648 −0.0905074 0 0.361288 1.00000 −0.0412395
1.12 0.622647 1.00000 −1.61231 −2.16920 0.622647 0 −2.24919 1.00000 −1.35064
1.13 1.06975 1.00000 −0.855631 −2.20739 1.06975 0 −3.05482 1.00000 −2.36136
1.14 1.11936 1.00000 −0.747042 4.03875 1.11936 0 −3.07492 1.00000 4.52079
1.15 1.53890 1.00000 0.368216 2.37632 1.53890 0 −2.51115 1.00000 3.65692
1.16 1.70195 1.00000 0.896650 −1.43807 1.70195 0 −1.87785 1.00000 −2.44754
1.17 2.10218 1.00000 2.41916 3.14040 2.10218 0 0.881157 1.00000 6.60169
1.18 2.16204 1.00000 2.67440 −2.94715 2.16204 0 1.45808 1.00000 −6.37183
1.19 2.43160 1.00000 3.91267 0.370755 2.43160 0 4.65084 1.00000 0.901528
1.20 2.51215 1.00000 4.31088 3.63202 2.51215 0 5.80526 1.00000 9.12418
See all 21 embeddings
\(n\): e.g. 2-40 or 990-1000
Embeddings: e.g. 1-3 or 1.21
Significant digits:
Format:

Atkin-Lehner signs

\( p \) Sign
\(3\) \( -1 \)
\(7\) \( -1 \)
\(61\) \( -1 \)

Inner twists

This newform does not admit any (nontrivial) inner twists.

Twists

       By twisting character orbit
Char Parity Ord Mult Type Twist Min Dim
1.a even 1 1 trivial 8967.2.a.bl 21
7.b odd 2 1 8967.2.a.bk 21
7.d odd 6 2 1281.2.j.i ✓ 42
    
        By twisted newform orbit
Twist Min Dim Char Parity Ord Mult Type
1281.2.j.i ✓ 42 7.d odd 6 2
8967.2.a.bk 21 7.b odd 2 1
8967.2.a.bl 21 1.a even 1 1 trivial

Hecke kernels

This newform subspace can be constructed as the intersection of the kernels of the following linear operators acting on \(S_{2}^{\mathrm{new}}(\Gamma_0(8967))\):

\( T_{2}^{21} - 37 T_{2}^{19} + 587 T_{2}^{17} + 4 T_{2}^{16} - 5234 T_{2}^{15} - 101 T_{2}^{14} + \cdots + 1995 \) Copy content Toggle raw display
\( T_{5}^{21} - 11 T_{5}^{20} - 2 T_{5}^{19} + 391 T_{5}^{18} - 733 T_{5}^{17} - 5882 T_{5}^{16} + \cdots - 68244 \) Copy content Toggle raw display
\( T_{11}^{21} - T_{11}^{20} - 137 T_{11}^{19} + 183 T_{11}^{18} + 7672 T_{11}^{17} - 12264 T_{11}^{16} + \cdots - 2773109415 \) Copy content Toggle raw display