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Properties

Label 12138.2.a.j
Level $12138$
Weight $2$
Character orbit 12138.a
Self dual yes
Analytic conductor $96.922$
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] = [12138,2,Mod(1,12138)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)
 
Copy content sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(12138, 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("12138.1"); S:= CuspForms(chi, 2); N := Newforms(S);
 
Level: \( N \) \(=\) \( 12138 = 2 \cdot 3 \cdot 7 \cdot 17^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 12138.a (trivial)

Newform invariants

Copy content comment:select newform
 
Copy content sage:traces = [1,-1,1,1,-2,-1,1,-1,1,2,6,1,0,-1,-2,1,0,-1,-2,-2,1,-6,0,-1,-1, 0,1,1,4,2,0,-1,6,0,-2,1,-8,2,0,2,-2,-1,-4,6,-2,0,-8,1,1,1,0,0,-14,-1,-12, -1,-2,-4,-6,-2,10,0,1,1,0,-6,0,0,0,2,12,-1,-14,8,-1,-2,6,0,-4,-2,1,2,-6, 1,0,4,4,-6,-14,2,0,0,0,8,4,-1,6,-1,6,-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: \(96.9224179734\)
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)
 
\(f(q)\) \(=\) \( q - q^{2} + q^{3} + q^{4} - 2 q^{5} - q^{6} + q^{7} - q^{8} + q^{9} + 2 q^{10} + 6 q^{11} + q^{12} - q^{14} - 2 q^{15} + q^{16} - q^{18} - 2 q^{19} - 2 q^{20} + q^{21} - 6 q^{22} - q^{24}+ \cdots + 6 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Atkin-Lehner signs

\( p \) Sign
\(2\) \( +1 \)
\(3\) \( -1 \)
\(7\) \( -1 \)
\(17\) \( +1 \)

Inner twists

Inner twists of this newform have not been computed.

Twists

Twists of this newform have not been computed.