Properties

Label 20339.2.a.l
Level $20339$
Weight $2$
Character orbit 20339.a
Self dual yes
Analytic conductor $162.408$
Dimension $11$

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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 = [11,1,-6,13,-3,5,-17,3,17,2,-11,-7,11,-12,8,13,-5,25,-5,-8,1, -1,11,8,16,13,-24,-34,16,1,33,12,6,3,9,2,-8,-6,-4,-45,2,-12,0,-13,-9,-13, 15,-6,20,-18,10,45,-5,-51,3,-14,4,6,4,-12,12,44,-18,-7,21,-5,32,-8,11, -1,-6,49,-10,-10,-16,42,17,-1,52,14,7,12,-29,-73,20,0,-19,-3,-5,-18,-22, 11,11,10,-22,-7,37,28,-17,-5] 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: \(11\)
Coefficient field: \(\mathbb{Q}[x]/(x^{11} - \cdots)\)
Copy content comment:defining polynomial
 
Copy content gp:f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{11} - x^{10} - 17x^{9} + 15x^{8} + 102x^{7} - 77x^{6} - 255x^{5} + 150x^{4} + 248x^{3} - 59x^{2} - 93x - 18 \) 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.

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