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Properties

Label 20070.2.a.e
Level $20070$
Weight $2$
Character orbit 20070.a
Self dual yes
Analytic conductor $160.260$
Dimension $1$

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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 = [1,-1,0,1,-1,0,0,-1,0,1,-1,0,4,0,0,1,5,0,-1,-1,0,1,5,0,1,-4,0, 0,-3,0,2,-1,0,-5,0,0,-9,1,0,1,-4,0,-12,-1,0,-5,0,0,-7,-1,0,4,12,0,1,0, 0,3,1,0,13,-2,0,1,-4,0,-15,5,0,0,14,0,-14,9,0,-1,0,0,-3,-1,0,4,4,0,-5, 12,0,1,8,0,0,5,0,0,1,0,2,7,0,1] 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: \(1\)
Coefficient field: \(\mathbb{Q}\)
Coefficient ring: \(\mathbb{Z}\)
Coefficient ring index: \( 1 \)
Twist minimal: not computed
Fricke sign: \(+1\)
Sato-Tate group: $\mathrm{SU}(2)$

$q$-expansion

Copy content comment:q-expansion
 
Copy content sage:f.q_expansion() # note that sage often uses an isomorphic number field
 
Copy content gp:mfcoefs(f, 20)
 
\(f(q)\) \(=\) \( q - q^{2} + q^{4} - q^{5} - q^{8} + q^{10} - q^{11} + 4 q^{13} + q^{16} + 5 q^{17} - q^{19} - q^{20} + q^{22} + 5 q^{23} + q^{25} - 4 q^{26} - 3 q^{29} + 2 q^{31} - q^{32} - 5 q^{34} - 9 q^{37}+ \cdots + 7 q^{98}+O(q^{100}) \) 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.