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Properties

Label 20339.2.a.f
Level $20339$
Weight $2$
Character orbit 20339.a
Self dual yes
Analytic conductor $162.408$
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] = [20339,2,Mod(1,20339)] 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("20339.1"); S:= CuspForms(chi, 2); N := Newforms(S);
 
Copy content sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(20339, base_ring=CyclotomicField(2)) chi = DirichletCharacter(H, H._module([0, 0])) N = Newforms(chi, 2, names="a")
 
Level: \( N \) \(=\) \( 20339 = 11 \cdot 43^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 20339.a (trivial)

Newform invariants

Copy content comment:select newform
 
Copy content sage:traces = [1,2,1,2,-1,2,2,0,-2,-2,1,2,4,4,-1,-4,-2,-4,0,-2,2,2,-1,0,-4, 8,-5,4,0,-2,7,-8,1,-4,-2,-4,-3,0,4,0,-8,4,0,2,2,-2,8,-4,-3,-8,-2,8,-6, -10,-1,0,0,0,5,-2,-12,14,-4,-8,-4,2,-7,-4,-1,-4,3,0,-4,-6,-4,0,2,8,-10, 4,1,-16,-6,4,2,0,0,0,-15,4,8,-2,7,16,0,-8,-7,-6,-2,-8] 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: \(162.407732671\)
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)
 
\(f(q)\) \(=\) \( q + 2 q^{2} + q^{3} + 2 q^{4} - q^{5} + 2 q^{6} + 2 q^{7} - 2 q^{9} - 2 q^{10} + q^{11} + 2 q^{12} + 4 q^{13} + 4 q^{14} - q^{15} - 4 q^{16} - 2 q^{17} - 4 q^{18} - 2 q^{20} + 2 q^{21} + 2 q^{22} - q^{23}+ \cdots - 2 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Atkin-Lehner signs

\( p \) Sign
\(11\) \( -1 \)
\(43\) \( -1 \)

Inner twists

Inner twists of this newform have not been computed.

Twists

Twists of this newform have not been computed.