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Properties

Label 62.6.d.a
Level $62$
Weight $6$
Character orbit 62.d
Analytic conductor $9.944$
Analytic rank $0$
Dimension $24$
Inner twists $2$

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Newspace parameters

Copy content comment:Compute space of new eigenforms
 
Copy content gp:[N,k,chi] = [62,6,Mod(33,62)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)
 
Copy content sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(62, base_ring=CyclotomicField(10)) chi = DirichletCharacter(H, H._module([8])) N = Newforms(chi, 6, names="a")
 
Copy content magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("62.33"); S:= CuspForms(chi, 6); N := Newforms(S);
 
Level: \( N \) \(=\) \( 62 = 2 \cdot 31 \)
Weight: \( k \) \(=\) \( 6 \)
Character orbit: \([\chi]\) \(=\) 62.d (of order \(5\), degree \(4\), minimal)

Newform invariants

Copy content comment:select newform
 
Copy content sage:traces = [24,-24] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(2)] == traces)
 
Copy content gp:f = lf[1] \\ Warning: the index may be different
 
Self dual: no
Analytic conductor: \(9.94379682840\)
Analytic rank: \(0\)
Dimension: \(24\)
Relative dimension: \(6\) over \(\Q(\zeta_{5})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{5}]$

$q$-expansion

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

\(\operatorname{Tr}(f)(q) = \) \( 24 q - 24 q^{2} - 20 q^{3} - 96 q^{4} + 120 q^{5} + 280 q^{6} - 180 q^{7} - 384 q^{8} - 200 q^{9} - 100 q^{10} + 354 q^{11} - 320 q^{12} + 39 q^{13} - 720 q^{14} + 535 q^{15} - 1536 q^{16} - 1027 q^{17}+ \cdots + 339042 q^{99}+O(q^{100}) \) 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.

Copy content comment:embeddings in the coefficient field
 
Copy content gp:mfembed(f)
 
Label   \( a_{2} \) \( a_{3} \) \( a_{4} \) \( a_{5} \) \( a_{6} \) \( a_{7} \) \( a_{8} \) \( a_{9} \) \( a_{10} \)
33.1 −3.23607 − 2.35114i −20.9547 + 15.2245i 4.94427 + 15.2169i 78.8224 103.606 −0.961853 − 2.96028i 19.7771 − 60.8676i 132.224 − 406.944i −255.075 − 185.323i
33.2 −3.23607 − 2.35114i −11.7313 + 8.52330i 4.94427 + 15.2169i −25.7786 58.0028 46.2201 + 142.251i 19.7771 − 60.8676i −10.1139 + 31.1275i 83.4214 + 60.6092i
33.3 −3.23607 − 2.35114i −10.5221 + 7.64478i 4.94427 + 15.2169i −86.6672 52.0243 −58.6301 − 180.445i 19.7771 − 60.8676i −22.8185 + 70.2280i 280.461 + 203.767i
33.4 −3.23607 − 2.35114i −1.20326 + 0.874217i 4.94427 + 15.2169i 11.0150 5.94923 −24.5773 − 75.6410i 19.7771 − 60.8676i −74.4076 + 229.003i −35.6452 − 25.8978i
33.5 −3.23607 − 2.35114i 10.2581 − 7.45295i 4.94427 + 15.2169i 64.6757 −50.7189 40.4673 + 124.545i 19.7771 − 60.8676i −25.4089 + 78.2004i −209.295 − 152.062i
33.6 −3.23607 − 2.35114i 19.0910 − 13.8704i 4.94427 + 15.2169i −14.3033 −94.3913 −43.0460 − 132.482i 19.7771 − 60.8676i 96.9871 − 298.496i 46.2864 + 33.6291i
35.1 1.23607 + 3.80423i −6.59038 + 20.2831i −12.9443 + 9.40456i −48.6693 −85.3076 4.11428 − 2.98920i −51.7771 − 37.6183i −171.380 − 124.515i −60.1585 − 185.149i
35.2 1.23607 + 3.80423i −4.18804 + 12.8895i −12.9443 + 9.40456i 43.2705 −54.2112 −148.915 + 108.193i −51.7771 − 37.6183i 47.9922 + 34.8684i 53.4853 + 164.611i
35.3 1.23607 + 3.80423i −0.518674 + 1.59632i −12.9443 + 9.40456i 52.9627 −6.71386 102.405 − 74.4014i −51.7771 − 37.6183i 194.312 + 141.176i 65.4655 + 201.482i
35.4 1.23607 + 3.80423i 2.72835 − 8.39700i −12.9443 + 9.40456i −56.0877 35.3165 116.648 − 84.7498i −51.7771 − 37.6183i 133.525 + 97.0119i −69.3282 − 213.370i
35.5 1.23607 + 3.80423i 6.17234 − 18.9965i −12.9443 + 9.40456i −50.2806 79.8964 −60.1640 + 43.7117i −51.7771 − 37.6183i −126.178 − 91.6738i −62.1502 − 191.279i
35.6 1.23607 + 3.80423i 7.45871 − 22.9556i −12.9443 + 9.40456i 91.0405 96.5476 −63.5604 + 46.1794i −51.7771 − 37.6183i −274.734 − 199.606i 112.532 + 346.339i
39.1 1.23607 − 3.80423i −6.59038 − 20.2831i −12.9443 − 9.40456i −48.6693 −85.3076 4.11428 + 2.98920i −51.7771 + 37.6183i −171.380 + 124.515i −60.1585 + 185.149i
39.2 1.23607 − 3.80423i −4.18804 − 12.8895i −12.9443 − 9.40456i 43.2705 −54.2112 −148.915 − 108.193i −51.7771 + 37.6183i 47.9922 − 34.8684i 53.4853 − 164.611i
39.3 1.23607 − 3.80423i −0.518674 − 1.59632i −12.9443 − 9.40456i 52.9627 −6.71386 102.405 + 74.4014i −51.7771 + 37.6183i 194.312 − 141.176i 65.4655 − 201.482i
39.4 1.23607 − 3.80423i 2.72835 + 8.39700i −12.9443 − 9.40456i −56.0877 35.3165 116.648 + 84.7498i −51.7771 + 37.6183i 133.525 − 97.0119i −69.3282 + 213.370i
39.5 1.23607 − 3.80423i 6.17234 + 18.9965i −12.9443 − 9.40456i −50.2806 79.8964 −60.1640 − 43.7117i −51.7771 + 37.6183i −126.178 + 91.6738i −62.1502 + 191.279i
39.6 1.23607 − 3.80423i 7.45871 + 22.9556i −12.9443 − 9.40456i 91.0405 96.5476 −63.5604 − 46.1794i −51.7771 + 37.6183i −274.734 + 199.606i 112.532 − 346.339i
47.1 −3.23607 + 2.35114i −20.9547 − 15.2245i 4.94427 − 15.2169i 78.8224 103.606 −0.961853 + 2.96028i 19.7771 + 60.8676i 132.224 + 406.944i −255.075 + 185.323i
47.2 −3.23607 + 2.35114i −11.7313 − 8.52330i 4.94427 − 15.2169i −25.7786 58.0028 46.2201 − 142.251i 19.7771 + 60.8676i −10.1139 − 31.1275i 83.4214 − 60.6092i
See all 24 embeddings
\(n\): e.g. 2-40 or 990-1000
Embeddings: e.g. 1-3 or 33.6
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Inner twists

Char Parity Ord Mult Type
1.a even 1 1 trivial
31.d even 5 1 inner

Twists

       By twisting character orbit
Char Parity Ord Mult Type Twist Min Dim
1.a even 1 1 trivial 62.6.d.a ✓ 24
31.d even 5 1 inner 62.6.d.a ✓ 24
    
        By twisted newform orbit
Twist Min Dim Char Parity Ord Mult Type
62.6.d.a ✓ 24 1.a even 1 1 trivial
62.6.d.a ✓ 24 31.d even 5 1 inner

Hecke kernels

This newform subspace can be constructed as the kernel of the linear operator \( T_{3}^{24} + 20 T_{3}^{23} + 1029 T_{3}^{22} + 22055 T_{3}^{21} + 831184 T_{3}^{20} + \cdots + 20\!\cdots\!61 \) acting on \(S_{6}^{\mathrm{new}}(62, [\chi])\). Copy content Toggle raw display