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Properties

Label 17689.2.a.cu
Level $17689$
Weight $2$
Character orbit 17689.a
Self dual yes
Analytic conductor $141.247$
Dimension $30$

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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 = [30,-6,0,30,0,0,0,-18,30,0,0,0,0,0,-24,30,0,-6,0,0,0,-42,12,0, 30,0,0,0,-30,-90,0,-72,0,0,0,78,-12,0,24,0,0,0,12,-6,0,-12,0,0,0,-42,-36, 0,-42,0,0,0,0,-60,0,-12,0,0,0,42,-78,0,0,0,0,0,-72,-18,0,114,0,0,0,54, -84,0,-30,0,0,0,6,-54,0,-144,0,0,0,0,-48,0,0,0,0,0,-84,138] 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: \(30\)
Twist minimal: not computed
Fricke sign: \(+1\)
Sato-Tate group: not computed

$q$-expansion

The algebraic \(q\)-expansion of this newform has not been computed, but we have computed the trace expansion.

\(\operatorname{Tr}(f)(q) = \) \( 30 q - 6 q^{2} + 30 q^{4} - 18 q^{8} + 30 q^{9} - 24 q^{15} + 30 q^{16} - 6 q^{18} - 42 q^{22} + 12 q^{23} + 30 q^{25} - 30 q^{29} - 90 q^{30} - 72 q^{32} + 78 q^{36} - 12 q^{37} + 24 q^{39} + 12 q^{43}+ \cdots - 84 q^{99}+O(q^{100}) \) 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.