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Properties

Label 2808.2.cw.b
Level $2808$
Weight $2$
Character orbit 2808.cw
Analytic conductor $22.422$
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] = [2808,2,Mod(1585,2808)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)
 
Copy content sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(2808, 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("2808.1585"); S:= CuspForms(chi, 2); N := Newforms(S);
 
Level: \( N \) \(=\) \( 2808 = 2^{3} \cdot 3^{3} \cdot 13 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 2808.cw (of order \(6\), degree \(2\), not 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: \(22.4219928876\)
Analytic rank: \(0\)
Dimension: \(80\)
Relative dimension: \(40\) over \(\Q(\zeta_{6})\)
Twist minimal: no (minimal twist has level 936)
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.

\(\operatorname{Tr}(f)(q) = \) \( 80 q + 6 q^{13} + 4 q^{17} - 10 q^{23} + 44 q^{25} + 52 q^{35} - 26 q^{43} + 48 q^{49} - 60 q^{53} - 16 q^{55} - 10 q^{61} + 26 q^{65} - 32 q^{77} + 6 q^{79} - 4 q^{91} - 8 q^{95}+O(q^{100}) \) 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   \( a_{2} \) \( a_{3} \) \( a_{4} \) \( a_{5} \) \( a_{6} \) \( a_{7} \) \( a_{8} \) \( a_{9} \) \( a_{10} \)
1585.1 0 0 0 −3.67745 + 2.12318i 0 −1.50584 − 0.869395i 0 0 0
1585.2 0 0 0 −3.55302 + 2.05134i 0 −0.0747053 − 0.0431311i 0 0 0
1585.3 0 0 0 −3.40435 + 1.96550i 0 −4.16592 − 2.40520i 0 0 0
1585.4 0 0 0 −3.18952 + 1.84147i 0 0.115004 + 0.0663978i 0 0 0
1585.5 0 0 0 −2.92247 + 1.68729i 0 3.92087 + 2.26372i 0 0 0
1585.6 0 0 0 −2.49707 + 1.44169i 0 0.640571 + 0.369834i 0 0 0
1585.7 0 0 0 −2.47613 + 1.42959i 0 2.42039 + 1.39742i 0 0 0
1585.8 0 0 0 −2.35377 + 1.35895i 0 1.56404 + 0.902998i 0 0 0
1585.9 0 0 0 −1.98449 + 1.14575i 0 −4.38662 − 2.53262i 0 0 0
1585.10 0 0 0 −1.91469 + 1.10545i 0 −1.00877 − 0.582415i 0 0 0
1585.11 0 0 0 −1.55919 + 0.900198i 0 2.30144 + 1.32873i 0 0 0
1585.12 0 0 0 −1.43066 + 0.825993i 0 −3.63744 − 2.10008i 0 0 0
1585.13 0 0 0 −1.12193 + 0.647747i 0 1.01499 + 0.586005i 0 0 0
1585.14 0 0 0 −1.11041 + 0.641094i 0 2.57119 + 1.48448i 0 0 0
1585.15 0 0 0 −0.975646 + 0.563289i 0 −3.67745 − 2.12318i 0 0 0
1585.16 0 0 0 −0.896010 + 0.517312i 0 1.06580 + 0.615342i 0 0 0
1585.17 0 0 0 −0.834885 + 0.482021i 0 −2.67273 − 1.54310i 0 0 0
1585.18 0 0 0 −0.319679 + 0.184567i 0 −0.108726 − 0.0627730i 0 0 0
1585.19 0 0 0 −0.107804 + 0.0622405i 0 1.23873 + 0.715181i 0 0 0
1585.20 0 0 0 −0.0518638 + 0.0299436i 0 3.08098 + 1.77880i 0 0 0
See all 80 embeddings
\(n\): e.g. 2-40 or 990-1000
Embeddings: e.g. 1-3 or 1585.40
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 2808.2.cw.b 80
3.b odd 2 1 936.2.cw.b ✓ 80
9.c even 3 1 inner 2808.2.cw.b 80
9.d odd 6 1 936.2.cw.b ✓ 80
13.b even 2 1 inner 2808.2.cw.b 80
39.d odd 2 1 936.2.cw.b ✓ 80
117.n odd 6 1 936.2.cw.b ✓ 80
117.t even 6 1 inner 2808.2.cw.b 80
    
        By twisted newform orbit
Twist Min Dim Char Parity Ord Mult Type
936.2.cw.b ✓ 80 3.b odd 2 1
936.2.cw.b ✓ 80 9.d odd 6 1
936.2.cw.b ✓ 80 39.d odd 2 1
936.2.cw.b ✓ 80 117.n odd 6 1
2808.2.cw.b 80 1.a even 1 1 trivial
2808.2.cw.b 80 9.c even 3 1 inner
2808.2.cw.b 80 13.b even 2 1 inner
2808.2.cw.b 80 117.t even 6 1 inner

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 \(S_{2}^{\mathrm{new}}(2808, [\chi])\). Copy content Toggle raw display