↑

Properties

Label 16698.2.a.j
Level $16698$
Weight $2$
Character orbit 16698.a
Self dual yes
Analytic conductor $133.334$
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] = [16698,2,Mod(1,16698)] 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("16698.1"); S:= CuspForms(chi, 2); N := Newforms(S);
 
Copy content sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(16698, base_ring=CyclotomicField(2)) chi = DirichletCharacter(H, H._module([0, 0, 0])) N = Newforms(chi, 2, names="a")
 
Level: \( N \) \(=\) \( 16698 = 2 \cdot 3 \cdot 11^{2} \cdot 23 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 16698.a (trivial)

Newform invariants

Copy content comment:select newform
 
Copy content sage:traces = [1,-1,-1,1,2,1,0,-1,1,-2,0,-1,2,0,-2,1,-2,-1,8,2,0,0,-1,1,-1, -2,-1,0,2,2,-8,-1,0,2,0,1,2,-8,-2,-2,-10,0,-8,0,2,1,8,-1,-7,1,2,2,2,1, 0,0,-8,-2,-4,-2,-2,8,0,1,4,0,8,-2,1,0,0,-1,6,-2,1,8,0,2,-8,2,1,10,16,0, -4,8,-2,0,18,-2,0,-1,8,-8,16,1,10,7,0,-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: \(133.334201295\)
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)
 
\(f(q)\) \(=\) \( q - q^{2} - q^{3} + q^{4} + 2 q^{5} + q^{6} - q^{8} + q^{9} - 2 q^{10} - q^{12} + 2 q^{13} - 2 q^{15} + q^{16} - 2 q^{17} - q^{18} + 8 q^{19} + 2 q^{20} - q^{23} + q^{24} - q^{25} - 2 q^{26}+ \cdots + 7 q^{98}+O(q^{100}) \) Copy content Toggle raw display

Atkin-Lehner signs

\( p \) Sign
\(2\) \( +1 \)
\(3\) \( +1 \)
\(11\) \( -1 \)
\(23\) \( +1 \)

Inner twists

Inner twists of this newform have not been computed.

Twists

Twists of this newform have not been computed.