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Properties

Label 20070.2.a.bu
Level $20070$
Weight $2$
Character orbit 20070.a
Self dual yes
Analytic conductor $160.260$
Dimension $3$

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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 = [3,-3,0,3,3,0,4,-3,0,-3,5,0,-11,-4,0,3,10,0,-2,3,0,-5,-6,0,3, 11,0,4,-7,0,0,-3,0,-10,4,0,2,2,0,-3,-2,0,1,5,0,6,-2,0,-1,-3,0,-11,-23, 0,5,-4,0,7,-14,0,10,0,0,3,-11,0,29,10,0,-4,-20,0,12,-2,0,-2,-3,0,-34,3, 0,2,-27,0,10,-1,0,-5,10,0,0,-6,0,2,-2,0,-8,1,0,3] 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: \(3\)
Coefficient field: 3.3.1509.1
Copy content comment:defining polynomial
 
Copy content gp:f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{3} - x^{2} - 7x + 4 \) 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.

\(\operatorname{Tr}(f)(q) = \) \( 3 q - 3 q^{2} + 3 q^{4} + 3 q^{5} + 4 q^{7} - 3 q^{8} - 3 q^{10} + 5 q^{11} - 11 q^{13} - 4 q^{14} + 3 q^{16} + 10 q^{17} - 2 q^{19} + 3 q^{20} - 5 q^{22} - 6 q^{23} + 3 q^{25} + 11 q^{26} + 4 q^{28} - 7 q^{29}+ \cdots + q^{98}+O(q^{100}) \) 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.