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Properties

Label 182.3.k.a
Level $182$
Weight $3$
Character orbit 182.k
Analytic conductor $4.959$
Analytic rank $0$
Dimension $36$
Inner twists $2$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [182,3,Mod(101,182)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(182, base_ring=CyclotomicField(6))
 
chi = DirichletCharacter(H, H._module([1, 5]))
 
N = Newforms(chi, 3, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("182.101");
 
S:= CuspForms(chi, 3);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 182 = 2 \cdot 7 \cdot 13 \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 182.k (of order \(6\), 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: \(4.95914081136\)
Analytic rank: \(0\)
Dimension: \(36\)
Relative dimension: \(18\) over \(\Q(\zeta_{6})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{6}]$

$q$-expansion

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

\(\operatorname{Tr}(f)(q) = \) \( 36 q + 36 q^{4} + 10 q^{7} - 88 q^{9} - 12 q^{12} - 4 q^{13} - 12 q^{14} + 60 q^{15} - 72 q^{16} + 24 q^{17} - 24 q^{18} + 100 q^{19} - 42 q^{21} + 12 q^{22} + 28 q^{23} - 82 q^{25} + 120 q^{26} + 4 q^{28}+ \cdots + 96 q^{98}+O(q^{100}) \) 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   \( a_{2} \) \( a_{3} \) \( a_{4} \) \( a_{5} \) \( a_{6} \) \( a_{7} \) \( a_{8} \) \( a_{9} \) \( a_{10} \)
101.1 −1.22474 − 0.707107i − 5.39170i 1.00000 + 1.73205i 1.60444 + 2.77896i −3.81251 + 6.60346i −6.78200 − 1.73332i − 2.82843i −20.0704 − 4.53803i
101.2 −1.22474 − 0.707107i − 3.15670i 1.00000 + 1.73205i 2.18358 + 3.78206i −2.23213 + 3.86616i 5.93564 + 3.71055i − 2.82843i −0.964772 − 6.17609i
101.3 −1.22474 − 0.707107i − 2.74178i 1.00000 + 1.73205i −0.905631 − 1.56860i −1.93873 + 3.35798i 6.97908 − 0.540725i − 2.82843i 1.48266 2.56151i
101.4 −1.22474 − 0.707107i − 0.464638i 1.00000 + 1.73205i 0.913880 + 1.58289i −0.328548 + 0.569062i −5.23853 − 4.64303i − 2.82843i 8.78411 − 2.58484i
101.5 −1.22474 − 0.707107i 0.599163i 1.00000 + 1.73205i −2.93203 − 5.07842i 0.423672 − 0.733822i −6.63379 + 2.23447i − 2.82843i 8.64100 8.29303i
101.6 −1.22474 − 0.707107i 0.997088i 1.00000 + 1.73205i −2.39328 − 4.14528i 0.705048 − 1.22118i 0.359568 + 6.99076i − 2.82843i 8.00582 6.76921i
101.7 −1.22474 − 0.707107i 2.61846i 1.00000 + 1.73205i 3.10639 + 5.38043i 1.85153 − 3.20695i 2.61741 − 6.49224i − 2.82843i 2.14365 − 8.78621i
101.8 −1.22474 − 0.707107i 4.37470i 1.00000 + 1.73205i 2.56440 + 4.44167i 3.09338 − 5.35789i 2.86286 + 6.38780i − 2.82843i −10.1380 − 7.25322i
101.9 −1.22474 − 0.707107i 4.89745i 1.00000 + 1.73205i −4.14175 − 7.17372i 3.46302 − 5.99813i 4.84926 − 5.04824i − 2.82843i −14.9850 11.7146i
101.10 1.22474 + 0.707107i − 4.24411i 1.00000 + 1.73205i −2.97543 − 5.15360i 3.00104 − 5.19795i −6.87300 − 1.32736i 2.82843i −9.01248 − 8.41579i
101.11 1.22474 + 0.707107i − 3.98808i 1.00000 + 1.73205i 0.700844 + 1.21390i 2.82000 − 4.88438i 2.68579 − 6.46425i 2.82843i −6.90481 1.98229i
101.12 1.22474 + 0.707107i − 3.43880i 1.00000 + 1.73205i 3.24452 + 5.61967i 2.43160 − 4.21165i 3.70893 + 5.93665i 2.82843i −2.82532 9.17688i
101.13 1.22474 + 0.707107i − 0.262462i 1.00000 + 1.73205i −4.53203 − 7.84970i 0.185589 − 0.321449i 6.48718 + 2.62991i 2.82843i 8.93111 − 12.8185i
101.14 1.22474 + 0.707107i − 0.0568985i 1.00000 + 1.73205i 0.904458 + 1.56657i 0.0402333 − 0.0696861i 2.86528 − 6.38672i 2.82843i 8.99676 2.55819i
101.15 1.22474 + 0.707107i 0.265126i 1.00000 + 1.73205i 1.03292 + 1.78906i −0.187472 + 0.324711i −5.02643 + 4.87186i 2.82843i 8.92971 2.92153i
101.16 1.22474 + 0.707107i 3.89692i 1.00000 + 1.73205i 0.569657 + 0.986676i −2.75554 + 4.77274i 6.85176 + 1.43295i 2.82843i −6.18601 1.61123i
101.17 1.22474 + 0.707107i 4.02925i 1.00000 + 1.73205i 4.59702 + 7.96227i −2.84911 + 4.93480i −5.39829 − 4.45628i 2.82843i −7.23484 13.0023i
101.18 1.22474 + 0.707107i 5.53110i 1.00000 + 1.73205i −3.54195 − 6.13483i −3.91108 + 6.77419i −5.25071 + 4.62926i 2.82843i −21.5931 − 10.0181i
173.1 −1.22474 + 0.707107i − 4.89745i 1.00000 − 1.73205i −4.14175 + 7.17372i 3.46302 + 5.99813i 4.84926 + 5.04824i 2.82843i −14.9850 − 11.7146i
173.2 −1.22474 + 0.707107i − 4.37470i 1.00000 − 1.73205i 2.56440 − 4.44167i 3.09338 + 5.35789i 2.86286 − 6.38780i 2.82843i −10.1380 7.25322i
See all 36 embeddings
\(n\): e.g. 2-40 or 990-1000
Embeddings: e.g. 1-3 or 101.18
Significant digits:
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Inner twists

Char Parity Ord Mult Type
1.a even 1 1 trivial
91.p odd 6 1 inner

Twists

       By twisting character orbit
Char Parity Ord Mult Type Twist Min Dim
1.a even 1 1 trivial 182.3.k.a ✓ 36
7.d odd 6 1 182.3.r.a yes 36
13.e even 6 1 182.3.r.a yes 36
91.p odd 6 1 inner 182.3.k.a ✓ 36
    
        By twisted newform orbit
Twist Min Dim Char Parity Ord Mult Type
182.3.k.a ✓ 36 1.a even 1 1 trivial
182.3.k.a ✓ 36 91.p odd 6 1 inner
182.3.r.a yes 36 7.d odd 6 1
182.3.r.a yes 36 13.e even 6 1

Hecke kernels

This newform subspace is the entire newspace \(S_{3}^{\mathrm{new}}(182, [\chi])\).