↑

Properties

Label 17689.2.a.dh
Level $17689$
Weight $2$
Character orbit 17689.a
Self dual yes
Analytic conductor $141.247$
Dimension $64$

Related objects

Downloads

Learn more

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 = [64,0,0,44,0,0,0,0,24,0,-64,0,0,0,0,28,0,0,0,0,0,0,-80,0,32,0, 0,0,0,-104,0,0,0,0,0,68,0,0,-104,0,0,0,-56,-112,0,0,0,0,0,0,0,0,0,0,0, 0,0,-88,0,0,0,0,0,20,0,0,0,0,0,0,0,0,0,-64,0,0,0,0,0,0,-152,0,0,0,-56, 0,0,0,0,0,0,-132,-48,0,0,0,0,0,-168,-332] 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: \(64\)
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.

\(\operatorname{Tr}(f)(q) = \) \( 64 q + 44 q^{4} + 24 q^{9} - 64 q^{11} + 28 q^{16} - 80 q^{23} + 32 q^{25} - 104 q^{30} + 68 q^{36} - 104 q^{39} - 56 q^{43} - 112 q^{44} - 88 q^{58} + 20 q^{64} - 64 q^{74} - 152 q^{81} - 56 q^{85} - 132 q^{92}+ \cdots - 168 q^{99}+O(q^{100}) \) 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.