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Properties

Label 20339.2.a.bd
Level $20339$
Weight $2$
Character orbit 20339.a
Self dual yes
Analytic conductor $162.408$
Dimension $108$

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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 = [108,6,18,104,36,2,23,18,104,5,108,32,2,-20,0,96,0,-49,60,84, -11,6,6,6,96,76,78,66,30,38,2,57,18,96,14,74,115,-35,63,1,-10,40,0,104, 185,70,0,41,99,-23,48,-40,19,-69,36,-117,31,-11,-14,8,157,30,63,20,51, 2,3,-30,194,80,124,-119,79,-45,163,64,23,112,-43,149,96,120,34,-41,149, 0,-105,18,130,-83,93,-28,75,118,57,30,-1,-46,104,275] 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: \(108\)
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.

\(\operatorname{Tr}(f)(q) = \) \( 108 q + 6 q^{2} + 18 q^{3} + 104 q^{4} + 36 q^{5} + 2 q^{6} + 23 q^{7} + 18 q^{8} + 104 q^{9} + 5 q^{10} + 108 q^{11} + 32 q^{12} + 2 q^{13} - 20 q^{14} + 96 q^{16} - 49 q^{18} + 60 q^{19} + 84 q^{20} - 11 q^{21}+ \cdots + 104 q^{99}+O(q^{100}) \) 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.