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Properties

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

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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 = [2,1,-3,3,6,5,0,6,5,3,-5,2,-4,0,-9,-3,7,-17,0,9,0,4,-6,-9,8,-15, -18,0,-9,15,-1,-7,14,10,0,-12,0,0,-7,18,5,0,-20,-1,15,-3,2,11,0,4,-4,-19, 3,17,-15,0,0,-24,2,6,-6,6,0,-4,-12,-19,-7,17,9,0,-10,15,15,-13,-12,0,0, 3,-8,-9,38,-4,15,0,21,-10,-6,-15,-14,-51,0,-9,8,-25,0,4,12,0,-32,12] 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: \(2\)
Coefficient field: \(\Q(\sqrt{13}) \)
Copy content comment:defining polynomial
 
Copy content gp:f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{2} - x - 3 \) 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.

\(\operatorname{Tr}(f)(q) = \) \( 2 q + q^{2} - 3 q^{3} + 3 q^{4} + 6 q^{5} + 5 q^{6} + 6 q^{8} + 5 q^{9} + 3 q^{10} - 5 q^{11} + 2 q^{12} - 4 q^{13} - 9 q^{15} - 3 q^{16} + 7 q^{17} - 17 q^{18} + 9 q^{20} + 4 q^{22} - 6 q^{23} - 9 q^{24}+ \cdots - 32 q^{99}+O(q^{100}) \) 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.