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Properties

Label 20339.2.a.m
Level $20339$
Weight $2$
Character orbit 20339.a
Self dual yes
Analytic conductor $162.408$
Dimension $16$

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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 = [16,0,0,10,0,-4,0,0,20,0,-16,0,-2,-16,-6,-10,10,0,0,0,-18,0,-12, -18,8,0,0,0,0,0,8,0,0,0,26,-30,0,-4,0,-2,0,0,0,-10,0,0,38,0,2,0,0,50,-12, 16,0,0,-12,-10,-2,-44,0,0,0,-18,0,4,-46,68,0,0,0,0,0,36,0,0,0,-30,14,0, 44,0,-40,46,0,0,24,0,0,68,0,-42,0,0,44,16,-18,0,-20,2] 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: \(16\)
Coefficient field: \(\mathbb{Q}[x]/(x^{16} - \cdots)\)
Copy content comment:defining polynomial
 
Copy content gp:f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{16} - 21x^{14} + 176x^{12} - 756x^{10} + 1768x^{8} - 2185x^{6} + 1253x^{4} - 245x^{2} + 11 \) Copy content Toggle raw display
Twist minimal: not computed
Fricke sign: \(+1\)
Sato-Tate group: not computed

$q$-expansion

The algebraic \(q\)-expansion of this newform has not been computed, but we have computed the trace expansion.

\(\operatorname{Tr}(f)(q) = \) \( 16 q + 10 q^{4} - 4 q^{6} + 20 q^{9} - 16 q^{11} - 2 q^{13} - 16 q^{14} - 6 q^{15} - 10 q^{16} + 10 q^{17} - 18 q^{21} - 12 q^{23} - 18 q^{24} + 8 q^{25} + 8 q^{31} + 26 q^{35} - 30 q^{36} - 4 q^{38} - 2 q^{40}+ \cdots - 20 q^{99}+O(q^{100}) \) 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.