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Properties

Label 20339.2.a.v
Level $20339$
Weight $2$
Character orbit 20339.a
Self dual yes
Analytic conductor $162.408$
Dimension $57$

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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 = [57,3,12,61,18,-2,9,9,61,-5,57,28,-6,-16,0,69,0,94,20,21,-5,3, -9,-27,63,23,42,26,60,-23,-21,6,12,30,4,61,37,11,2,-46,-17,-34,0,61,49, 5,-3,40,44,5,-3,27,-19,117,18,18,-17,-7,-4,-56,82,-36,2,49,3,-2,-16,-9, 94,76,50,254,88,-75,47,157,9,134,-3,52,9,21,-43,-77,46,0,192,9,38,62,46, -32,44,56,-3,-72,39,37,61,148] 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: \(57\)
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.

\(\operatorname{Tr}(f)(q) = \) \( 57 q + 3 q^{2} + 12 q^{3} + 61 q^{4} + 18 q^{5} - 2 q^{6} + 9 q^{7} + 9 q^{8} + 61 q^{9} - 5 q^{10} + 57 q^{11} + 28 q^{12} - 6 q^{13} - 16 q^{14} + 69 q^{16} + 94 q^{18} + 20 q^{19} + 21 q^{20} - 5 q^{21}+ \cdots + 61 q^{99}+O(q^{100}) \) 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.