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Properties

Label 23670.2.a.k
Level $23670$
Weight $2$
Character orbit 23670.a
Self dual yes
Analytic conductor $189.006$
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] = [23670,2,Mod(1,23670)] 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("23670.1"); S:= CuspForms(chi, 2); N := Newforms(S);
 
Copy content sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(23670, base_ring=CyclotomicField(2)) chi = DirichletCharacter(H, H._module([0, 0, 0])) N = Newforms(chi, 2, names="a")
 
Level: \( N \) \(=\) \( 23670 = 2 \cdot 3^{2} \cdot 5 \cdot 263 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 23670.a (trivial)

Newform invariants

Copy content comment:select newform
 
Copy content sage:traces = [1,1,0,1,-1,0,-4,1,0,-1,-6,0,-1,-4,0,1,0,0,0,-1,0,-6,8,0,1,-1, 0,-4,3,0,7,1,0,0,4,0,-1,0,0,-1,0,0,-1,-6,0,8,1,0,9,1,0,-1,2,0,6,-4,0,3, 5,0,-2,7,0,1,1,0,-2,0,0,4,12,0,-10,-1,0,0,24,0,-8,-1,0,0,3,0,0,-1,0,-6, 10,0,4,8,0,1,0,0,-7,9,0,1] 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: \(189.005901584\)
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)
 
\(f(q)\) \(=\) \( q + q^{2} + q^{4} - q^{5} - 4 q^{7} + q^{8} - q^{10} - 6 q^{11} - q^{13} - 4 q^{14} + q^{16} - q^{20} - 6 q^{22} + 8 q^{23} + q^{25} - q^{26} - 4 q^{28} + 3 q^{29} + 7 q^{31} + q^{32} + 4 q^{35}+ \cdots + 9 q^{98}+O(q^{100}) \) Copy content Toggle raw display

Atkin-Lehner signs

\( p \) Sign
\(2\) \( -1 \)
\(3\) \( -1 \)
\(5\) \( +1 \)
\(263\) \( +1 \)

Inner twists

Inner twists of this newform have not been computed.

Twists

Twists of this newform have not been computed.