↑

Properties

Label 16606.2.a.f
Level $16606$
Weight $2$
Character orbit 16606.a
Self dual yes
Analytic conductor $132.600$
Dimension $1$

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] = [16606,2,Mod(1,16606)] 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("16606.1"); S:= CuspForms(chi, 2); N := Newforms(S);
 
Copy content sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(16606, base_ring=CyclotomicField(2)) chi = DirichletCharacter(H, H._module([0, 0])) N = Newforms(chi, 2, names="a")
 
Level: \( N \) \(=\) \( 16606 = 2 \cdot 19^{2} \cdot 23 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 16606.a (trivial)

Newform invariants

Copy content comment:select newform
 
Copy content sage:traces = [1,-1,-1,1,3,1,2,-1,-2,-3,-3,-1,-2,-2,-3,1,0,2,0,3,-2,3,1,1,4, 2,5,2,3,3,4,-1,3,0,6,-2,4,0,2,-3,-6,2,-13,-3,-6,-1,3,-1,-3,-4,0,-2,0,-5, -9,-2,0,-3,-9,-3,2,-4,-4,1,-6,-3,-8,0,-1,-6,12,2,11,-4,-4,0,-6,-2,1,3, 1,6,9,-2,0,13,-3,3,3,6,-4,1,-4,-3,0,1,-17,3,6,4] 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: \(132.599577597\)
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)
 
\(f(q)\) \(=\) \( q - q^{2} - q^{3} + q^{4} + 3 q^{5} + q^{6} + 2 q^{7} - q^{8} - 2 q^{9} - 3 q^{10} - 3 q^{11} - q^{12} - 2 q^{13} - 2 q^{14} - 3 q^{15} + q^{16} + 2 q^{18} + 3 q^{20} - 2 q^{21} + 3 q^{22} + q^{23}+ \cdots + 6 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Atkin-Lehner signs

\( p \) Sign
\(2\) \( +1 \)
\(19\) \( -1 \)
\(23\) \( -1 \)

Inner twists

Inner twists of this newform have not been computed.

Twists

Twists of this newform have not been computed.