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Properties

Label 29640.2.a.br
Level $29640$
Weight $2$
Character orbit 29640.a
Self dual yes
Analytic conductor $236.677$
Dimension $12$
CM no
Inner twists $1$

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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] = [29640,2,Mod(1,29640)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)
 
Copy content sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(29640, base_ring=CyclotomicField(2)) chi = DirichletCharacter(H, H._module([0, 0, 0, 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("29640.1"); S:= CuspForms(chi, 2); N := Newforms(S);
 
Level: \( N \) \(=\) \( 29640 = 2^{3} \cdot 3 \cdot 5 \cdot 13 \cdot 19 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 29640.a (trivial)

Newform invariants

Copy content comment:select newform
 
Copy content sage:traces = [12,0,12,0,-12,0,0,0,12,0,-2,0,12,0,-12,0,10,0,-12,0,0,0,-9,0, 12,0,12,0,7,0,18,0,-2,0,0,0,16,0,12,0,11,0,18,0,-12,0,-15,0,30,0,10,0, 5,0,2,0,-12,0,12,0,2,0,0,0,-12,0,38,0,-9,0,0,0,-26,0,12,0,-8,0,17,0,12, 0,12,0,-10,0,7,0,-16,0,0,0,18,0,12,0,-3,0,-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: \(236.676591591\)
Dimension: \(12\)
Coefficient field: \(\mathbb{Q}[x]/(x^{12} - \cdots)\)
Copy content comment:defining polynomial
 
Copy content gp:f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{12} - 2 x^{11} - 41 x^{10} + 38 x^{9} + 635 x^{8} + 21 x^{7} - 4223 x^{6} - 2936 x^{5} + 10966 x^{4} + \cdots - 4544 \) Copy content Toggle raw display
Twist minimal: yes
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.

\(\operatorname{Tr}(f)(q) = \) \( 12 q + 12 q^{3} - 12 q^{5} + 12 q^{9} - 2 q^{11} + 12 q^{13} - 12 q^{15} + 10 q^{17} - 12 q^{19} - 9 q^{23} + 12 q^{25} + 12 q^{27} + 7 q^{29} + 18 q^{31} - 2 q^{33} + 16 q^{37} + 12 q^{39} + 11 q^{41}+ \cdots - 2 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Atkin-Lehner signs

\( p \) Sign
\(2\) \( -1 \)
\(3\) \( -1 \)
\(5\) \( +1 \)
\(13\) \( -1 \)
\(19\) \( +1 \)

Inner twists

This newform does not admit any (nontrivial) inner twists.

Twists

Twists of this newform have not been computed.