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Properties

Label 20339.2.a.e
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,-2,0,0,-2,2,-1,-2,-2,0,-1,-4,6,-4,8,2,0,-2,-1,0,-4, -4,5,0,-6,-2,-1,-8,1,12,0,-4,3,16,2,0,-4,0,0,-2,-2,-2,-8,4,-7,-8,-6,-4, -14,10,-1,0,-8,-12,9,-2,4,-2,0,-8,-2,2,9,12,1,0,13,0,16,6,4,16,0,4,16, -4,1,-8,-6,0,6,0,6,0,7,-4,0,-2,1,-16,8,8,13,-14,2,-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)
 
\(f(q)\) \(=\) \( q + 2 q^{2} - q^{3} + 2 q^{4} + q^{5} - 2 q^{6} - 2 q^{9} + 2 q^{10} - q^{11} - 2 q^{12} - 2 q^{13} - q^{15} - 4 q^{16} + 6 q^{17} - 4 q^{18} + 8 q^{19} + 2 q^{20} - 2 q^{22} - q^{23} - 4 q^{25} - 4 q^{26}+ \cdots + 2 q^{99}+O(q^{100}) \) 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.