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Properties

Label 32186.2.a.m
Level $32186$
Weight $2$
Character orbit 32186.a
Self dual yes
Analytic conductor $257.007$
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] = [32186,2,Mod(1,32186)] 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("32186.1"); S:= CuspForms(chi, 2); N := Newforms(S);
 
Copy content sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(32186, base_ring=CyclotomicField(2)) chi = DirichletCharacter(H, H._module([0, 0, 0])) N = Newforms(chi, 2, names="a")
 
Level: \( N \) \(=\) \( 32186 = 2 \cdot 7 \cdot 11^{2} \cdot 19 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 32186.a (trivial)

Newform invariants

Copy content comment:select newform
 
Copy content sage:traces = [1,-1,2,1,2,-2,-1,-1,1,-2,0,2,0,1,4,1,-8,-1,-1,2,-2,0,-4,-2,-1, 0,-4,-1,-6,-4,-2,-1,0,8,-2,1,2,1,0,-2,12,2,-4,0,2,4,6,2,1,1,-16,0,-6,4, 0,1,-2,6,-6,4,8,2,-1,1,0,0,12,-8,-8,2,8,-1,4,-2,-2,-1,0,0,8,2,-11,-12, -4,-2,-16,4,-12,0,2,-2,0,-4,-4,-6,-2,-2,6,-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: \(257.006503946\)
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)
 
\(f(q)\) \(=\) \( q - q^{2} + 2 q^{3} + q^{4} + 2 q^{5} - 2 q^{6} - q^{7} - q^{8} + q^{9} - 2 q^{10} + 2 q^{12} + q^{14} + 4 q^{15} + q^{16} - 8 q^{17} - q^{18} - q^{19} + 2 q^{20} - 2 q^{21} - 4 q^{23} - 2 q^{24}+ \cdots - q^{98}+O(q^{100}) \) Copy content Toggle raw display

Atkin-Lehner signs

\( p \) Sign
\(2\) \( +1 \)
\(7\) \( +1 \)
\(11\) \( -1 \)
\(19\) \( +1 \)

Inner twists

Inner twists of this newform have not been computed.

Twists

Twists of this newform have not been computed.