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Properties

Label 3467.2.a.b
Level $3467$
Weight $2$
Character orbit 3467.a
Self dual yes
Analytic conductor $27.684$
Analytic rank $1$
Dimension $126$
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] = [3467,2,Mod(1,3467)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(3467, base_ring=CyclotomicField(2))
 
chi = DirichletCharacter(H, H._module([0]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("3467.1");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 3467 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 3467.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: \(27.6841343808\)
Analytic rank: \(1\)
Dimension: \(126\)
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.

\(\operatorname{Tr}(f)(q) = \) \( 126 q - 11 q^{2} - 25 q^{3} + 99 q^{4} - 32 q^{5} - 15 q^{6} - 27 q^{7} - 27 q^{8} + 93 q^{9} - 46 q^{10} - 6 q^{11} - 67 q^{12} - 137 q^{13} - 17 q^{14} - 15 q^{15} + 49 q^{16} - 30 q^{17} - 37 q^{18}+ \cdots + 9 q^{99}+O(q^{100}) \) 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 −2.81889 1.88995 5.94612 0.0344178 −5.32754 0.0210525 −11.1236 0.571893 −0.0970198
1.2 −2.70199 −2.09860 5.30076 4.30988 5.67040 1.11728 −8.91864 1.40411 −11.6453
1.3 −2.65255 −2.93902 5.03600 −0.874862 7.79587 −1.75901 −8.05313 5.63781 2.32061
1.4 −2.59942 −0.00337391 4.75700 0.594552 0.00877021 −0.0975981 −7.16662 −2.99999 −1.54549
1.5 −2.59264 −3.37242 4.72177 0.980667 8.74347 0.391354 −7.05657 8.37323 −2.54251
1.6 −2.58136 −1.91872 4.66342 0.890273 4.95291 −3.20311 −6.87523 0.681498 −2.29811
1.7 −2.57298 −0.267298 4.62023 −2.52986 0.687753 −4.69728 −6.74181 −2.92855 6.50927
1.8 −2.53407 −0.0627431 4.42150 1.25371 0.158995 4.70847 −6.13625 −2.99606 −3.17699
1.9 −2.52387 −1.17627 4.36993 −2.77279 2.96875 1.50723 −5.98139 −1.61639 6.99817
1.10 −2.51087 2.31262 4.30446 0.617108 −5.80669 −3.50171 −5.78621 2.34822 −1.54948
1.11 −2.44912 1.51788 3.99820 3.38472 −3.71747 −0.262313 −4.89384 −0.696042 −8.28959
1.12 −2.41383 2.94587 3.82656 −1.24422 −7.11083 −1.16259 −4.40901 5.67816 3.00333
1.13 −2.34534 −0.641042 3.50064 2.05340 1.50346 2.98302 −3.51951 −2.58907 −4.81592
1.14 −2.30915 −2.10535 3.33217 0.0313740 4.86157 0.850976 −3.07619 1.43250 −0.0724474
1.15 −2.25286 1.81709 3.07540 0.961173 −4.09365 −3.61685 −2.42273 0.301811 −2.16539
1.16 −2.23448 −2.02465 2.99292 2.52351 4.52405 −3.87648 −2.21866 1.09920 −5.63873
1.17 −2.20044 −1.79291 2.84195 −2.03691 3.94519 3.67495 −1.85267 0.214519 4.48210
1.18 −2.16722 −0.211282 2.69686 −1.75495 0.457895 −1.86583 −1.51026 −2.95536 3.80337
1.19 −2.13193 1.56803 2.54511 −1.31271 −3.34293 2.51209 −1.16213 −0.541279 2.79859
1.20 −2.12058 1.70158 2.49684 2.03679 −3.60832 3.50112 −1.05359 −0.104638 −4.31916
See next 80 embeddings (of 126 total)
\(n\): e.g. 2-40 or 990-1000
Embeddings: e.g. 1-3 or 1.126
Significant digits:
Format:

Atkin-Lehner signs

\( p \) Sign
\(3467\) \( +1 \)

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 3467.2.a.b ✓ 126
    
        By twisted newform orbit
Twist Min Dim Char Parity Ord Mult Type
3467.2.a.b ✓ 126 1.a even 1 1 trivial

Hecke kernels

This newform subspace can be constructed as the kernel of the linear operator \( T_{2}^{126} + 11 T_{2}^{125} - 115 T_{2}^{124} - 1685 T_{2}^{123} + 5240 T_{2}^{122} + 124649 T_{2}^{121} + \cdots + 41591 \) acting on \(S_{2}^{\mathrm{new}}(\Gamma_0(3467))\). Copy content Toggle raw display