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Properties

Label 12138.2.a.cy
Level $12138$
Weight $2$
Character orbit 12138.a
Self dual yes
Analytic conductor $96.922$
Dimension $8$

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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 = [8,-8,-8,8,-12,8,-8,-8,8,12,-12,-8,12,8,12,8,0,-8,8,-12,8,12, -16,8,12,-12,-8,-8,-16,-12,8,-8,12,0,12,8,-4,-8,-12,12,-32,-8,12,-12,-12, 16,0,-8,8,-12,0,12,4,8,20,8,-8,16,0,12,-8,-8,-8,8,-20,-12,12,0,16,-12, -16,-8,12,4,-12,8,12,12,4,-12,8,32,4,8,0,-12,16,12,-4,12,-12,-16,-8,0, -16,8,12,-8,-12,12] 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: \(8\)
Coefficient field: 8.8.74360815616.1
Copy content comment:defining polynomial
 
Copy content gp:f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{8} - 4x^{7} - 10x^{6} + 44x^{5} + 33x^{4} - 144x^{3} - 48x^{2} + 128x + 32 \) 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.

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