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Properties

Label 17689.2.a.bb
Level $17689$
Weight $2$
Character orbit 17689.a
Self dual yes
Analytic conductor $141.247$
Dimension $3$

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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] = [17689,2,Mod(1,17689)] 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("17689.1"); S:= CuspForms(chi, 2); N := Newforms(S);
 
Copy content sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(17689, base_ring=CyclotomicField(2)) chi = DirichletCharacter(H, H._module([0, 0])) N = Newforms(chi, 2, names="a")
 
Level: \( N \) \(=\) \( 17689 = 7^{2} \cdot 19^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 17689.a (trivial)

Newform invariants

Copy content comment:select newform
 
Copy content sage:traces = [3,-2,3,6,2,1,0,-3,2,-9,7,-2,-2,0,7,-4,-7,-6,0,-1,0,6,14,13,-1, 9,6,0,3,-17,-11,-8,10,-12,0,-9,0,0,-7,8,-7,0,-4,11,19,-23,-8,-23,0,-1, -26,1,1,-33,-3,0,0,18,-10,-4,6,12,0,-5,-14,7,3,5,3,0,0,24,-1,29,20,0,0, 17,4,-5,-1,-24,-31,0,-7,18,-20,-1,-28,-19,0,39,-24,25,0,-6,-30,0,0,-23] 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: \(141.247376135\)
Dimension: \(3\)
Coefficient field: 3.3.229.1
Copy content comment:defining polynomial
 
Copy content gp:f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{3} - 4x - 1 \) 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.

\(\operatorname{Tr}(f)(q) = \) \( 3 q - 2 q^{2} + 3 q^{3} + 6 q^{4} + 2 q^{5} + q^{6} - 3 q^{8} + 2 q^{9} - 9 q^{10} + 7 q^{11} - 2 q^{12} - 2 q^{13} + 7 q^{15} - 4 q^{16} - 7 q^{17} - 6 q^{18} - q^{20} + 6 q^{22} + 14 q^{23} + 13 q^{24}+ \cdots - 30 q^{97}+O(q^{100}) \) Copy content Toggle raw display

Atkin-Lehner signs

\( p \) Sign
\(7\) \( -1 \)
\(19\) \( -1 \)

Inner twists

Inner twists of this newform have not been computed.

Twists

Twists of this newform have not been computed.