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Properties

Label 20339.2.a.n
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,-2,0,20,-5,-1,-2,0,17,2,-17,-21,-3,-15,3,18,3,9,-13,25,-24, 2,-1,19,20,19,-15,-7,-20,5,11,-17,0,-27,19,35,-8,-15,-2,-10,4,-5,0,-20, -9,17,2,-40,27,-6,5,-38,10,-6,5,-14,4,-5,14,-75,-9,-17,-19,-62,-2,1,10, 35,-7,-16,-17,2,-18,-6,-24,-51,2,-66,36,84,-15,4,16,-22,-48,0,60,0,-49, 165,-72,-4,-56,-2,-38,43,9,-107,-17,-28] 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: \( x^{17} - 2 x^{16} - 25 x^{15} + 50 x^{14} + 248 x^{13} - 501 x^{12} - 1224 x^{11} + 2541 x^{10} + \cdots - 3 \) 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.

\(\operatorname{Tr}(f)(q) = \) \( 17 q - 2 q^{2} + 20 q^{4} - 5 q^{5} - q^{6} - 2 q^{7} + 17 q^{9} + 2 q^{10} - 17 q^{11} - 21 q^{12} - 3 q^{13} - 15 q^{14} + 3 q^{15} + 18 q^{16} + 3 q^{17} + 9 q^{18} - 13 q^{19} + 25 q^{20} - 24 q^{21}+ \cdots - 17 q^{99}+O(q^{100}) \) 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.