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Properties

Label 17689.2.a.cy
Level $17689$
Weight $2$
Character orbit 17689.a
Self dual yes
Analytic conductor $141.247$
Dimension $33$

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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 = [33,0,-9,24,3,-6,0,6,18,0,0,-27,-12,0,-9,6,-6,18,0,0,0,0,12,-12, 6,-9,-30,0,0,-3,-39,12,-24,-12,0,-24,-6,0,24,-12,-48,0,21,6,3,-6,21,18, 0,-27,30,-48,6,0,-18,0,0,42,-60,42,3,-33,0,-24,-21,-6,-18,15,-42,0,12, 33,-9,18,-57,0,0,-30,-9,27,9,18,18,0,42,-6,9,45,-84,-6,0,24,48,-72,0,-69, 15,0,54,-60] 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: \(33\)
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.

\(\operatorname{Tr}(f)(q) = \) \( 33 q - 9 q^{3} + 24 q^{4} + 3 q^{5} - 6 q^{6} + 6 q^{8} + 18 q^{9} - 27 q^{12} - 12 q^{13} - 9 q^{15} + 6 q^{16} - 6 q^{17} + 18 q^{18} + 12 q^{23} - 12 q^{24} + 6 q^{25} - 9 q^{26} - 30 q^{27} - 3 q^{30}+ \cdots + 54 q^{99}+O(q^{100}) \) 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.