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Properties

Label 936.2.cw.b
Level $936$
Weight $2$
Character orbit 936.cw
Analytic conductor $7.474$
Analytic rank $0$
Dimension $80$
Inner twists $4$

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Newspace parameters

Copy content comment:Compute space of new eigenforms
 
Copy content gp:[N,k,chi] = [936,2,Mod(25,936)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)
 
Copy content sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(936, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([0, 0, 4, 3])) N = Newforms(chi, 2, names="a")
 
Copy content magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("936.25"); S:= CuspForms(chi, 2); N := Newforms(S);
 
Level: \( N \) \(=\) \( 936 = 2^{3} \cdot 3^{2} \cdot 13 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 936.cw (of order \(6\), degree \(2\), minimal)

Newform invariants

Copy content comment:select newform
 
Copy content sage:traces = [80] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(1)] == traces)
 
Copy content gp:f = lf[1] \\ Warning: the index may be different
 
Self dual: no
Analytic conductor: \(7.47399762919\)
Analytic rank: \(0\)
Dimension: \(80\)
Relative dimension: \(40\) 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.

\(\operatorname{Tr}(f)(q) = \) \( 80 q - 6 q^{3} - 6 q^{9} + 6 q^{13} - 4 q^{17} + 10 q^{23} + 44 q^{25} + 6 q^{27} - 52 q^{35} + 40 q^{39} - 26 q^{43} + 48 q^{49} + 36 q^{51} + 60 q^{53} - 16 q^{55} - 10 q^{61} - 26 q^{65} - 38 q^{69}+ \cdots + 8 q^{95}+O(q^{100}) \) 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   \( a_{2} \) \( a_{3} \) \( a_{4} \) \( a_{5} \) \( a_{6} \) \( a_{7} \) \( a_{8} \) \( a_{9} \) \( a_{10} \)
25.1 0 −1.73126 + 0.0522212i 0 −2.92247 + 1.68729i 0 −3.92087 − 2.26372i 0 2.99455 − 0.180817i 0
25.2 0 −1.73126 + 0.0522212i 0 2.92247 − 1.68729i 0 3.92087 + 2.26372i 0 2.99455 − 0.180817i 0
25.3 0 −1.64480 + 0.542809i 0 −1.91469 + 1.10545i 0 1.00877 + 0.582415i 0 2.41072 − 1.78562i 0
25.4 0 −1.64480 + 0.542809i 0 1.91469 − 1.10545i 0 −1.00877 − 0.582415i 0 2.41072 − 1.78562i 0
25.5 0 −1.57632 − 0.717780i 0 −0.834885 + 0.482021i 0 2.67273 + 1.54310i 0 1.96958 + 2.26290i 0
25.6 0 −1.57632 − 0.717780i 0 0.834885 − 0.482021i 0 −2.67273 − 1.54310i 0 1.96958 + 2.26290i 0
25.7 0 −1.46835 − 0.918660i 0 −2.49707 + 1.44169i 0 −0.640571 − 0.369834i 0 1.31213 + 2.69784i 0
25.8 0 −1.46835 − 0.918660i 0 2.49707 − 1.44169i 0 0.640571 + 0.369834i 0 1.31213 + 2.69784i 0
25.9 0 −1.33894 + 1.09874i 0 −1.98449 + 1.14575i 0 4.38662 + 2.53262i 0 0.585535 − 2.94230i 0
25.10 0 −1.33894 + 1.09874i 0 1.98449 − 1.14575i 0 −4.38662 − 2.53262i 0 0.585535 − 2.94230i 0
25.11 0 −1.33331 + 1.10556i 0 −1.12193 + 0.647747i 0 −1.01499 − 0.586005i 0 0.555454 − 2.94813i 0
25.12 0 −1.33331 + 1.10556i 0 1.12193 − 0.647747i 0 1.01499 + 0.586005i 0 0.555454 − 2.94813i 0
25.13 0 −0.919549 − 1.46780i 0 −0.975646 + 0.563289i 0 3.67745 + 2.12318i 0 −1.30886 + 2.69942i 0
25.14 0 −0.919549 − 1.46780i 0 0.975646 − 0.563289i 0 −3.67745 − 2.12318i 0 −1.30886 + 2.69942i 0
25.15 0 −0.628838 − 1.61387i 0 −3.18952 + 1.84147i 0 −0.115004 − 0.0663978i 0 −2.20913 + 2.02972i 0
25.16 0 −0.628838 − 1.61387i 0 3.18952 − 1.84147i 0 0.115004 + 0.0663978i 0 −2.20913 + 2.02972i 0
25.17 0 −0.530837 + 1.64870i 0 −2.35377 + 1.35895i 0 −1.56404 − 0.902998i 0 −2.43642 − 1.75038i 0
25.18 0 −0.530837 + 1.64870i 0 2.35377 − 1.35895i 0 1.56404 + 0.902998i 0 −2.43642 − 1.75038i 0
25.19 0 −0.365445 + 1.69306i 0 −0.107804 + 0.0622405i 0 −1.23873 − 0.715181i 0 −2.73290 − 1.23744i 0
25.20 0 −0.365445 + 1.69306i 0 0.107804 − 0.0622405i 0 1.23873 + 0.715181i 0 −2.73290 − 1.23744i 0
See all 80 embeddings
\(n\): e.g. 2-40 or 990-1000
Embeddings: e.g. 1-3 or 25.40
Significant digits:
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Inner twists

Char Parity Ord Mult Type
1.a even 1 1 trivial
9.c even 3 1 inner
13.b even 2 1 inner
117.t even 6 1 inner

Twists

       By twisting character orbit
Char Parity Ord Mult Type Twist Min Dim
1.a even 1 1 trivial 936.2.cw.b ✓ 80
3.b odd 2 1 2808.2.cw.b 80
9.c even 3 1 inner 936.2.cw.b ✓ 80
9.d odd 6 1 2808.2.cw.b 80
13.b even 2 1 inner 936.2.cw.b ✓ 80
39.d odd 2 1 2808.2.cw.b 80
117.n odd 6 1 2808.2.cw.b 80
117.t even 6 1 inner 936.2.cw.b ✓ 80
    
        By twisted newform orbit
Twist Min Dim Char Parity Ord Mult Type
936.2.cw.b ✓ 80 1.a even 1 1 trivial
936.2.cw.b ✓ 80 9.c even 3 1 inner
936.2.cw.b ✓ 80 13.b even 2 1 inner
936.2.cw.b ✓ 80 117.t even 6 1 inner
2808.2.cw.b 80 3.b odd 2 1
2808.2.cw.b 80 9.d odd 6 1
2808.2.cw.b 80 39.d odd 2 1
2808.2.cw.b 80 117.n odd 6 1

Hecke kernels

This newform subspace can be constructed as the kernel of the linear operator \( T_{5}^{80} - 122 T_{5}^{78} + 8157 T_{5}^{76} - 376440 T_{5}^{74} + 13245432 T_{5}^{72} + \cdots + 4746193387776 \) acting on \(S_{2}^{\mathrm{new}}(936, [\chi])\). Copy content Toggle raw display