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Properties

Label 3283.2.a.bd
Level $3283$
Weight $2$
Character orbit 3283.a
Self dual yes
Analytic conductor $26.215$
Analytic rank $1$
Dimension $26$
Inner twists $2$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [3283,2,Mod(1,3283)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(3283, base_ring=CyclotomicField(2))
 
chi = DirichletCharacter(H, H._module([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("3283.1");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 3283 = 7^{2} \cdot 67 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 3283.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: \(26.2148869836\)
Analytic rank: \(1\)
Dimension: \(26\)
Twist minimal: yes
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.

\(\operatorname{Tr}(f)(q) = \) \( 26 q - 10 q^{2} + 30 q^{4} - 54 q^{8} + 14 q^{9}+O(q^{10}) \) Copy content Toggle raw display
\(\operatorname{Tr}(f)(q) = \) \( 26 q - 10 q^{2} + 30 q^{4} - 54 q^{8} + 14 q^{9} - 24 q^{11} - 24 q^{15} + 30 q^{16} - 38 q^{18} + 20 q^{22} - 16 q^{23} + 14 q^{25} - 60 q^{29} - 16 q^{30} - 78 q^{32} + 70 q^{36} - 64 q^{37} - 12 q^{39} - 8 q^{43} - 56 q^{44} - 16 q^{46} - 22 q^{50} - 44 q^{51} - 128 q^{53} - 56 q^{57} + 8 q^{58} - 68 q^{60} + 122 q^{64} - 60 q^{65} - 26 q^{67} - 44 q^{71} - 154 q^{72} - 44 q^{74} - 28 q^{78} - 32 q^{79} - 54 q^{81} - 56 q^{85} - 44 q^{86} + 60 q^{88} - 116 q^{92} - 116 q^{93} - 76 q^{95} - 56 q^{99}+O(q^{100}) \) 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   \( a_{2} \) \( a_{3} \) \( a_{4} \) \( a_{5} \) \( a_{6} \) \( a_{7} \) \( a_{8} \) \( a_{9} \) \( a_{10} \)
1.1 −2.79947 −1.56741 5.83703 3.47097 4.38791 0 −10.7417 −0.543230 −9.71689
1.2 −2.79947 1.56741 5.83703 −3.47097 −4.38791 0 −10.7417 −0.543230 9.71689
1.3 −2.72605 −3.10780 5.43136 −0.233964 8.47203 0 −9.35407 6.65843 0.637798
1.4 −2.72605 3.10780 5.43136 0.233964 −8.47203 0 −9.35407 6.65843 −0.637798
1.5 −2.29507 −1.49725 3.26734 −1.76092 3.43628 0 −2.90862 −0.758253 4.04143
1.6 −2.29507 1.49725 3.26734 1.76092 −3.43628 0 −2.90862 −0.758253 −4.04143
1.7 −1.99098 −2.44466 1.96399 1.11171 4.86727 0 0.0716934 2.97637 −2.21338
1.8 −1.99098 2.44466 1.96399 −1.11171 −4.86727 0 0.0716934 2.97637 2.21338
1.9 −1.54552 −2.05015 0.388624 0.958458 3.16854 0 2.49041 1.20310 −1.48131
1.10 −1.54552 2.05015 0.388624 −0.958458 −3.16854 0 2.49041 1.20310 1.48131
1.11 −1.37161 −1.08545 −0.118685 −4.05654 1.48882 0 2.90601 −1.82179 5.56399
1.12 −1.37161 1.08545 −0.118685 4.05654 −1.48882 0 2.90601 −1.82179 −5.56399
1.13 0.116687 −0.821338 −1.98638 −3.87267 −0.0958394 0 −0.465159 −2.32540 −0.451889
1.14 0.116687 0.821338 −1.98638 3.87267 0.0958394 0 −0.465159 −2.32540 0.451889
1.15 0.205284 −0.124696 −1.95786 2.23297 −0.0255981 0 −0.812485 −2.98445 0.458393
1.16 0.205284 0.124696 −1.95786 −2.23297 0.0255981 0 −0.812485 −2.98445 −0.458393
1.17 0.677130 −2.46325 −1.54149 0.887651 −1.66794 0 −2.39805 3.06758 0.601056
1.18 0.677130 2.46325 −1.54149 −0.887651 1.66794 0 −2.39805 3.06758 −0.601056
1.19 1.39081 −2.74533 −0.0656443 2.14165 −3.81824 0 −2.87292 4.53684 2.97863
1.20 1.39081 2.74533 −0.0656443 −2.14165 3.81824 0 −2.87292 4.53684 −2.97863
See all 26 embeddings
\(n\): e.g. 2-40 or 990-1000
Embeddings: e.g. 1-3 or 1.26
Significant digits:
Format:

Atkin-Lehner signs

\( p \) Sign
\(7\) \( +1 \)
\(67\) \( +1 \)

Inner twists

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

Twists

       By twisting character orbit
Char Parity Ord Mult Type Twist Min Dim
1.a even 1 1 trivial 3283.2.a.bd ✓ 26
7.b odd 2 1 inner 3283.2.a.bd ✓ 26
    
        By twisted newform orbit
Twist Min Dim Char Parity Ord Mult Type
3283.2.a.bd ✓ 26 1.a even 1 1 trivial
3283.2.a.bd ✓ 26 7.b odd 2 1 inner

Hecke kernels

This newform subspace can be constructed as the intersection of the kernels of the following linear operators acting on \(S_{2}^{\mathrm{new}}(\Gamma_0(3283))\):

\( T_{2}^{13} + 5 T_{2}^{12} - 8 T_{2}^{11} - 66 T_{2}^{10} + 6 T_{2}^{9} + 334 T_{2}^{8} + 83 T_{2}^{7} + \cdots - 9 \) Copy content Toggle raw display
\( T_{3}^{26} - 46 T_{3}^{24} + 923 T_{3}^{22} - 10652 T_{3}^{20} + 78481 T_{3}^{18} - 387316 T_{3}^{16} + \cdots - 1568 \) Copy content Toggle raw display