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Properties

Label 18207.2.a.e
Level $18207$
Weight $2$
Character orbit 18207.a
Self dual yes
Analytic conductor $145.384$
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] = [18207,2,Mod(1,18207)] 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("18207.1"); S:= CuspForms(chi, 2); N := Newforms(S);
 
Copy content sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(18207, base_ring=CyclotomicField(2)) chi = DirichletCharacter(H, H._module([0, 0, 0])) N = Newforms(chi, 2, names="a")
 
Level: \( N \) \(=\) \( 18207 = 3^{2} \cdot 7 \cdot 17^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 18207.a (trivial)

Newform invariants

Copy content comment:select newform
 
Copy content sage:traces = [1,1,0,-1,-2,0,1,-3,0,-2,4,0,-2,1,0,-1,0,0,4,2,0,4,0,0,-1,-2, 0,-1,-2,0,0,5,0,0,-2,0,-6,4,0,6,2,0,-4,-4,0,0,0,0,1,-1,0,2,-6,0,-8,-3, 0,-2,-12,0,2,0,0,7,4,0,4,0,0,-2,0,0,6,-6,0,-4,4,0,16,2,0,2,12,0,0,-4,0, -12,14,0,-2,0,0,0,-8,0,-18,1,0,1] 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: \(145.383626960\)
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)
 
\(f(q)\) \(=\) \( q + q^{2} - q^{4} - 2 q^{5} + q^{7} - 3 q^{8} - 2 q^{10} + 4 q^{11} - 2 q^{13} + q^{14} - q^{16} + 4 q^{19} + 2 q^{20} + 4 q^{22} - q^{25} - 2 q^{26} - q^{28} - 2 q^{29} + 5 q^{32} - 2 q^{35} - 6 q^{37}+ \cdots + q^{98}+O(q^{100}) \) Copy content Toggle raw display

Atkin-Lehner signs

\( p \) Sign
\(3\) \( -1 \)
\(7\) \( -1 \)
\(17\) \( +1 \)

Inner twists

Inner twists of this newform have not been computed.

Twists

Twists of this newform have not been computed.