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Properties

Label 18590.2.a.h
Level $18590$
Weight $2$
Character orbit 18590.a
Self dual yes
Analytic conductor $148.442$
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] = [18590,2,Mod(1,18590)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)
 
Copy content sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(18590, base_ring=CyclotomicField(2)) chi = DirichletCharacter(H, H._module([0, 0, 0])) N = Newforms(chi, 2, names="a")
 
Copy content magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("18590.1"); S:= CuspForms(chi, 2); N := Newforms(S);
 
Level: \( N \) \(=\) \( 18590 = 2 \cdot 5 \cdot 11 \cdot 13^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 18590.a (trivial)

Newform invariants

Copy content comment:select newform
 
Copy content sage:traces = [1,-1,2,1,-1,-2,-4,-1,1,1,1,2,0,4,-2,1,-2,-1,0,-1,-8,-1,-4,-2, 1,0,-4,-4,-8,2,0,-1,2,2,4,1,-6,0,0,1,8,8,4,1,-1,4,6,2,9,-1,-4,0,-4,4,-1, 4,0,8,-4,-2,8,0,-4,1,0,-2,12,-2,-8,-4,-16,-1,2,6,2,0,-4,0,-12,-1,-11,-8, 4,-8,2,-4,-16,-1,-6,1,0,-4,0,-6,0,-2,-12,-9,1,1] 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: \(148.441897358\)
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)
 
\(f(q)\) \(=\) \( q - q^{2} + 2 q^{3} + q^{4} - q^{5} - 2 q^{6} - 4 q^{7} - q^{8} + q^{9} + q^{10} + q^{11} + 2 q^{12} + 4 q^{14} - 2 q^{15} + q^{16} - 2 q^{17} - q^{18} - q^{20} - 8 q^{21} - q^{22} - 4 q^{23}+ \cdots + q^{99}+O(q^{100}) \) Copy content Toggle raw display

Atkin-Lehner signs

\( p \) Sign
\(2\) \( +1 \)
\(5\) \( +1 \)
\(11\) \( -1 \)
\(13\) \( +1 \)

Inner twists

Inner twists of this newform have not been computed.

Twists

Twists of this newform have not been computed.