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Properties

Label 16562.2.a.g
Level $16562$
Weight $2$
Character orbit 16562.a
Self dual yes
Analytic conductor $132.248$
Dimension $1$

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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] = [16562,2,Mod(1,16562)] 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("16562.1"); S:= CuspForms(chi, 2); N := Newforms(S);
 
Copy content sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(16562, base_ring=CyclotomicField(2)) chi = DirichletCharacter(H, H._module([0, 0])) N = Newforms(chi, 2, names="a")
 
Level: \( N \) \(=\) \( 16562 = 2 \cdot 7^{2} \cdot 13^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 16562.a (trivial)

Newform invariants

Copy content comment:select newform
 
Copy content sage:traces = [1,-1,-1,1,-2,1,0,-1,-2,2,5,-1,0,0,2,1,8,2,-8,-2,0,-5,7,1,-1, 0,5,0,6,-2,5,-1,-5,-8,0,-2,-1,8,0,2,9,0,2,5,4,-7,-3,-1,0,1,-8,0,10,-5, -10,0,8,-6,4,2,7,-5,0,1,0,5,5,8,-7,0,14,2,-11,1,1,-8,0,0,-11,-2,1,-9,14, 0,-16,-2,-6,-5,-6,-4,0,7,-5,3,16,1,-13,0,-10,-1] 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: \(132.248235828\)
Dimension: \(1\)
Coefficient field: \(\mathbb{Q}\)
Coefficient ring: \(\mathbb{Z}\)
Coefficient ring index: \( 1 \)
Twist minimal: not computed
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

$q$-expansion

Copy content comment:q-expansion
 
Copy content sage:f.q_expansion() # note that sage often uses an isomorphic number field
 
Copy content gp:mfcoefs(f, 20)
 
\(f(q)\) \(=\) \( q - q^{2} - q^{3} + q^{4} - 2 q^{5} + q^{6} - q^{8} - 2 q^{9} + 2 q^{10} + 5 q^{11} - q^{12} + 2 q^{15} + q^{16} + 8 q^{17} + 2 q^{18} - 8 q^{19} - 2 q^{20} - 5 q^{22} + 7 q^{23} + q^{24} - q^{25}+ \cdots - 10 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Atkin-Lehner signs

\( p \) Sign
\(2\) \( +1 \)
\(7\) \( -1 \)
\(13\) \( +1 \)

Inner twists

Inner twists of this newform have not been computed.

Twists

Twists of this newform have not been computed.