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Properties

Label 12138.2.a.ct
Level $12138$
Weight $2$
Character orbit 12138.a
Self dual yes
Analytic conductor $96.922$
Dimension $6$

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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 = [6,6,6,6,-9,6,-6,6,6,-9,-3,6,-3,-6,-9,6,0,6,6,-9,-6,-3,-12,6, 3,-3,6,-6,-12,-9,-3,6,-3,0,9,6,3,6,-3,-9,-24,-6,-12,-3,-9,-12,6,6,6,3, 0,-3,-6,6,0,-6,6,-12,30,-9,-24,-3,-6,6,0,-3,-18,0,-12,9,-21,6,-33,3,3, 6,3,-3,-3,-9,6,-24,-24,-6,0,-12,-12,-3,0,-9,3,-12,-3,6,-42,6,-12,6,-3, 3] 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: \(6\)
Coefficient field: 6.6.7328637.1
Copy content comment:defining polynomial
 
Copy content gp:f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{6} - 3x^{5} - 6x^{4} + 16x^{3} + 12x^{2} - 18x - 3 \) 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.

\(\operatorname{Tr}(f)(q) = \) \( 6 q + 6 q^{2} + 6 q^{3} + 6 q^{4} - 9 q^{5} + 6 q^{6} - 6 q^{7} + 6 q^{8} + 6 q^{9} - 9 q^{10} - 3 q^{11} + 6 q^{12} - 3 q^{13} - 6 q^{14} - 9 q^{15} + 6 q^{16} + 6 q^{18} + 6 q^{19} - 9 q^{20} - 6 q^{21}+ \cdots - 3 q^{99}+O(q^{100}) \) 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.