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Properties

Label 20339.2.a.p
Level $20339$
Weight $2$
Character orbit 20339.a
Self dual yes
Analytic conductor $162.408$
Dimension $17$

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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 = [17,0,2,16,7,-3,8,6,17,-4,17,25,-3,23,1,10,3,-19,3,13,0,0,-11, -3,20,7,11,15,-6,-9,5,-13,2,33,25,15,20,-21,-8,-4,8,19,0,16,-5,23,-18, 86,11,48,11,-22,-14,-24,7,24,4,7,-2,-9,27,5,15,50,6,-3,0,-15,-3,-6,57, -90,-2,54,-12,13,8,48,2,4,1,4,-32,-4,44,0,10,6,79,-31,78,-2,44,-10,20, -105,17,23,17,36] 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: \(17\)
Coefficient field: \(\mathbb{Q}[x]/(x^{17} - \cdots)\)
Copy content comment:defining polynomial
 
Copy content gp:f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{17} - 25 x^{15} - 2 x^{14} + 252 x^{13} + 43 x^{12} - 1324 x^{11} - 355 x^{10} + 3896 x^{9} + \cdots + 9 \) Copy content Toggle raw display
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.

\(\operatorname{Tr}(f)(q) = \) \( 17 q + 2 q^{3} + 16 q^{4} + 7 q^{5} - 3 q^{6} + 8 q^{7} + 6 q^{8} + 17 q^{9} - 4 q^{10} + 17 q^{11} + 25 q^{12} - 3 q^{13} + 23 q^{14} + q^{15} + 10 q^{16} + 3 q^{17} - 19 q^{18} + 3 q^{19} + 13 q^{20}+ \cdots + 17 q^{99}+O(q^{100}) \) 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.