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Properties

Label 1160.4.g.b
Level $1160$
Weight $4$
Character orbit 1160.g
Analytic conductor $68.442$
Analytic rank $0$
Dimension $46$
Inner twists $2$

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Show commands: Magma / Pari/GP / SageMath

Newspace parameters

Copy content comment:Compute space of new eigenforms
 
Copy content gp:[N,k,chi] = [1160,4,Mod(521,1160)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)
 
Copy content magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("1160.521"); S:= CuspForms(chi, 4); N := Newforms(S);
 
Copy content sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(1160, base_ring=CyclotomicField(2)) chi = DirichletCharacter(H, H._module([0, 0, 0, 1])) N = Newforms(chi, 4, names="a")
 
Level: \( N \) \(=\) \( 1160 = 2^{3} \cdot 5 \cdot 29 \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 1160.g (of order \(2\), degree \(1\), minimal)

Newform invariants

Copy content comment:select newform
 
Copy content sage:traces = [46] 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: \(68.4422156067\)
Analytic rank: \(0\)
Dimension: \(46\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

$q$-expansion

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

\(\operatorname{Tr}(f)(q) = \) \( 46 q - 230 q^{5} - 42 q^{7} - 512 q^{9} - 78 q^{13} - 214 q^{23} + 1150 q^{25} - 190 q^{29} - 796 q^{33} + 210 q^{35} + 2560 q^{45} + 1824 q^{49} + 240 q^{51} + 902 q^{53} - 2064 q^{57} - 734 q^{59} + 176 q^{63}+ \cdots + 104 q^{93}+O(q^{100}) \) 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   \( a_{2} \) \( a_{3} \) \( a_{4} \) \( a_{5} \) \( a_{6} \) \( a_{7} \) \( a_{8} \) \( a_{9} \) \( a_{10} \)
521.1 0 − 10.1764i 0 −5.00000 0 −1.69453 0 −76.5589 0
521.2 0 − 10.1480i 0 −5.00000 0 −24.3155 0 −75.9828 0
521.3 0 − 9.12158i 0 −5.00000 0 13.8913 0 −56.2032 0
521.4 0 − 8.76928i 0 −5.00000 0 23.9719 0 −49.9003 0
521.5 0 − 8.33230i 0 −5.00000 0 28.1107 0 −42.4272 0
521.6 0 − 8.24689i 0 −5.00000 0 7.04168 0 −41.0112 0
521.7 0 − 8.06000i 0 −5.00000 0 −17.7873 0 −37.9635 0
521.8 0 − 7.00296i 0 −5.00000 0 0.168012 0 −22.0415 0
521.9 0 − 6.21161i 0 −5.00000 0 −27.2721 0 −11.5841 0
521.10 0 − 5.99856i 0 −5.00000 0 −30.2274 0 −8.98278 0
521.11 0 − 5.80224i 0 −5.00000 0 −24.2503 0 −6.66600 0
521.12 0 − 5.73533i 0 −5.00000 0 2.92998 0 −5.89399 0
521.13 0 − 5.40559i 0 −5.00000 0 12.1410 0 −2.22041 0
521.14 0 − 4.96238i 0 −5.00000 0 −10.1723 0 2.37474 0
521.15 0 − 4.34224i 0 −5.00000 0 24.8166 0 8.14495 0
521.16 0 − 4.33136i 0 −5.00000 0 23.6847 0 8.23929 0
521.17 0 − 3.31881i 0 −5.00000 0 −35.5842 0 15.9855 0
521.18 0 − 2.72644i 0 −5.00000 0 −5.96809 0 19.5665 0
521.19 0 − 1.65208i 0 −5.00000 0 16.4272 0 24.2706 0
521.20 0 − 1.61896i 0 −5.00000 0 −13.2205 0 24.3790 0
See all 46 embeddings
\(n\): e.g. 2-40 or 990-1000
Embeddings: e.g. 1-3 or 521.46
Significant digits:
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Inner twists

Char Parity Ord Mult Type
1.a even 1 1 trivial
29.b even 2 1 inner

Twists

       By twisting character orbit
Char Parity Ord Mult Type Twist Min Dim
1.a even 1 1 trivial 1160.4.g.b ✓ 46
29.b even 2 1 inner 1160.4.g.b ✓ 46
    
        By twisted newform orbit
Twist Min Dim Char Parity Ord Mult Type
1160.4.g.b ✓ 46 1.a even 1 1 trivial
1160.4.g.b ✓ 46 29.b even 2 1 inner