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Properties

Label 12138.2.a.bv
Level $12138$
Weight $2$
Character orbit 12138.a
Self dual yes
Analytic conductor $96.922$
Dimension $2$

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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 = [2,2,2,2,0,2,-2,2,2,0,-2,2,-4,-2,0,2,0,2,-6,0,-2,-2,-2,2,0,-4, 2,-2,0,0,16,2,-2,0,0,2,-6,-6,-4,0,14,-2,-2,-2,0,-2,2,2,2,0,0,-4,0,2,20, -2,-6,0,10,0,-6,16,-2,2,20,-2,-2,0,-2,0,2,2,22,-6,0,-6,2,-4,8,0,2,14,-20, -2,0,-2,0,-2,-4,0,4,-2,16,2,10,2,18,2,-2,0] 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: \(2\)
Coefficient field: \(\Q(\sqrt{5}) \)
Copy content comment:defining polynomial
 
Copy content gp:f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{2} - x - 1 \) Copy content Toggle raw display
Twist minimal: not computed
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

$q$-expansion

The algebraic \(q\)-expansion of this newform has not been computed, but we have computed the trace expansion.

\(\operatorname{Tr}(f)(q) = \) \( 2 q + 2 q^{2} + 2 q^{3} + 2 q^{4} + 2 q^{6} - 2 q^{7} + 2 q^{8} + 2 q^{9} - 2 q^{11} + 2 q^{12} - 4 q^{13} - 2 q^{14} + 2 q^{16} + 2 q^{18} - 6 q^{19} - 2 q^{21} - 2 q^{22} - 2 q^{23} + 2 q^{24} - 4 q^{26}+ \cdots - 2 q^{99}+O(q^{100}) \) 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.