↑

Properties

Label 16170.2.a.bk
Level $16170$
Weight $2$
Character orbit 16170.a
Self dual yes
Analytic conductor $129.118$
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] = [16170,2,Mod(1,16170)] 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("16170.1"); S:= CuspForms(chi, 2); N := Newforms(S);
 
Copy content sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(16170, base_ring=CyclotomicField(2)) chi = DirichletCharacter(H, H._module([0, 0, 0, 0])) N = Newforms(chi, 2, names="a")
 
Level: \( N \) \(=\) \( 16170 = 2 \cdot 3 \cdot 5 \cdot 7^{2} \cdot 11 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 16170.a (trivial)

Newform invariants

Copy content comment:select newform
 
Copy content sage:traces = [1,1,-1,1,-1,-1,0,1,1,-1,-1,-1,2,0,1,1,-2,1,4,-1,0,-1,0,-1,1, 2,-1,0,-2,1,0,1,1,-2,0,1,-2,4,-2,-1,-2,0,-12,-1,-1,0,-8,-1,0,1,2,2,6,-1, 1,0,-4,-2,12,1,-6,0,0,1,-2,1,4,-2,0,0,0,1,6,-2,-1,4,0,-2,-16,-1,1,-2,-4, 0,2,-12,2,-1,-10,-1,0,0,0,-8,-4,-1,-2,0,-1,1] 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: \(129.118100068\)
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)
 
\(f(q)\) \(=\) \( q + q^{2} - q^{3} + q^{4} - q^{5} - q^{6} + q^{8} + q^{9} - q^{10} - q^{11} - q^{12} + 2 q^{13} + q^{15} + q^{16} - 2 q^{17} + q^{18} + 4 q^{19} - q^{20} - q^{22} - q^{24} + q^{25} + 2 q^{26}+ \cdots - q^{99}+O(q^{100}) \) Copy content Toggle raw display

Atkin-Lehner signs

\( p \) Sign
\(2\) \( -1 \)
\(3\) \( +1 \)
\(5\) \( +1 \)
\(7\) \( -1 \)
\(11\) \( +1 \)

Inner twists

Inner twists of this newform have not been computed.

Twists

Twists of this newform have not been computed.