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Properties

Label 20070.2.a.ct
Level $20070$
Weight $2$
Character orbit 20070.a
Self dual yes
Analytic conductor $160.260$
Dimension $9$

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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] = [20070,2,Mod(1,20070)] 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("20070.1"); S:= CuspForms(chi, 2); N := Newforms(S);
 
Copy content sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(20070, base_ring=CyclotomicField(2)) chi = DirichletCharacter(H, H._module([0, 0, 0])) N = Newforms(chi, 2, names="a")
 
Level: \( N \) \(=\) \( 20070 = 2 \cdot 3^{2} \cdot 5 \cdot 223 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 20070.a (trivial)

Newform invariants

Copy content comment:select newform
 
Copy content sage:traces = [9,9,0,9,-9,0,-7,9,0,-9,-5,0,-5,-7,0,9,8,0,-3,-9,0,-5,-1,0,9, -5,0,-7,8,0,7,9,0,8,7,0,-13,-3,0,-9,-16,0,-9,-5,0,-1,-17,0,8,9,0,-5,14, 0,5,-7,0,8,-28,0,2,7,0,9,5,0,6,8,0,7,-54,0,-23,-13,0,-3,29,0,10,-9,0,-16, -16,0,-8,-9,0,-5,-17,0,37,-1,0,-17,3,0,-15,8,0,9] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(None)] == traces)
 
Copy content gp:f = lf[1] \\ Warning: the index may be different
 
Self dual: yes
Analytic conductor: \(160.259756857\)
Dimension: \(9\)
Coefficient field: \(\mathbb{Q}[x]/(x^{9} - \cdots)\)
Copy content comment:defining polynomial
 
Copy content gp:f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{9} - 2x^{8} - 31x^{7} + 24x^{6} + 256x^{5} - 133x^{4} - 744x^{3} + 363x^{2} + 642x - 328 \) Copy content Toggle raw display
Twist minimal: not computed
Fricke sign: \(+1\)
Sato-Tate group: $\mathrm{SU}(2)$

$q$-expansion

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

\(\operatorname{Tr}(f)(q) = \) \( 9 q + 9 q^{2} + 9 q^{4} - 9 q^{5} - 7 q^{7} + 9 q^{8} - 9 q^{10} - 5 q^{11} - 5 q^{13} - 7 q^{14} + 9 q^{16} + 8 q^{17} - 3 q^{19} - 9 q^{20} - 5 q^{22} - q^{23} + 9 q^{25} - 5 q^{26} - 7 q^{28} + 8 q^{29}+ \cdots + 8 q^{98}+O(q^{100}) \) Copy content Toggle raw display

Atkin-Lehner signs

\( p \) Sign
\(2\) \( -1 \)
\(3\) \( -1 \)
\(5\) \( +1 \)
\(223\) \( +1 \)

Inner twists

Inner twists of this newform have not been computed.

Twists

Twists of this newform have not been computed.