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Properties

Label 3467.2.a.c
Level $3467$
Weight $2$
Character orbit 3467.a
Self dual yes
Analytic conductor $27.684$
Analytic rank $0$
Dimension $162$
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: \(0\)
Dimension: \(162\)
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.

\(\operatorname{Tr}(f)(q) = \) \( 162 q + 9 q^{2} + 24 q^{3} + 189 q^{4} + 32 q^{5} + 9 q^{6} + 23 q^{7} + 27 q^{8} + 196 q^{9} + 50 q^{10} + 12 q^{11} + 69 q^{12} + 144 q^{13} + 11 q^{14} + 17 q^{15} + 223 q^{16} + 33 q^{17} + 39 q^{18}+ \cdots - 25 q^{99}+O(q^{100}) \) 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 −2.77001 3.13539 5.67294 −3.74377 −8.68507 −2.59894 −10.1741 6.83070 10.3703
1.2 −2.76339 −1.19712 5.63632 −3.83920 3.30811 0.396758 −10.0486 −1.56690 10.6092
1.3 −2.75260 −1.14455 5.57679 3.26674 3.15048 −4.62962 −9.84547 −1.69001 −8.99203
1.4 −2.74906 −0.534947 5.55732 1.27817 1.47060 0.611481 −9.77929 −2.71383 −3.51376
1.5 −2.73871 1.92051 5.50054 3.55276 −5.25972 2.70752 −9.58697 0.688350 −9.72999
1.6 −2.72511 −2.47314 5.42623 0.222863 6.73958 4.75166 −9.33686 3.11642 −0.607327
1.7 −2.62421 0.535292 4.88647 −1.72546 −1.40472 −0.538039 −7.57470 −2.71346 4.52797
1.8 −2.60847 1.45556 4.80412 −1.44543 −3.79678 2.62404 −7.31448 −0.881354 3.77036
1.9 −2.60743 1.27566 4.79871 −3.17859 −3.32620 4.41798 −7.29746 −1.37269 8.28796
1.10 −2.58030 1.97569 4.65793 −3.02354 −5.09786 −2.06851 −6.85824 0.903346 7.80162
1.11 −2.55691 0.579978 4.53779 0.584541 −1.48295 −2.87828 −6.48889 −2.66363 −1.49462
1.12 −2.54044 3.12416 4.45382 2.16374 −7.93673 4.31506 −6.23377 6.76037 −5.49685
1.13 −2.54011 3.37616 4.45214 3.00973 −8.57581 −3.02513 −6.22871 8.39846 −7.64502
1.14 −2.52384 −2.22798 4.36975 −3.18933 5.62305 0.565198 −5.98088 1.96388 8.04935
1.15 −2.43856 0.828699 3.94656 3.17241 −2.02083 −0.797262 −4.74680 −2.31326 −7.73611
1.16 −2.41030 2.99235 3.80954 −2.37452 −7.21245 3.58446 −4.36154 5.95415 5.72329
1.17 −2.38469 −3.31861 3.68674 3.38333 7.91386 −1.46940 −4.02235 8.01318 −8.06818
1.18 −2.37064 −2.10307 3.61993 0.834031 4.98562 −2.35419 −3.84026 1.42290 −1.97719
1.19 −2.33790 −0.576512 3.46576 1.91248 1.34783 4.47693 −3.42681 −2.66763 −4.47118
1.20 −2.29213 −2.38838 3.25387 −2.03861 5.47448 2.45572 −2.87404 2.70435 4.67276
See next 80 embeddings (of 162 total)
\(n\): e.g. 2-40 or 990-1000
Embeddings: e.g. 1-3 or 1.162
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.c ✓ 162
    
        By twisted newform orbit
Twist Min Dim Char Parity Ord Mult Type
3467.2.a.c ✓ 162 1.a even 1 1 trivial

Hecke kernels

This newform subspace can be constructed as the kernel of the linear operator \( T_{2}^{162} - 9 T_{2}^{161} - 216 T_{2}^{160} + 2166 T_{2}^{159} + 22307 T_{2}^{158} + \cdots + 88\!\cdots\!56 \) acting on \(S_{2}^{\mathrm{new}}(\Gamma_0(3467))\). Copy content Toggle raw display