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Properties

Label 29640.2.a.bn
Level $29640$
Weight $2$
Character orbit 29640.a
Self dual yes
Analytic conductor $236.677$
Dimension $11$
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 = [11,0,11,0,11,0,-4,0,11,0,-7,0,-11,0,11,0,-6,0,11,0,-4,0,0,0, 11,0,11,0,-5,0,-13,0,-7,0,-4,0,-14,0,-11,0,-10,0,-9,0,11,0,-2,0,-7,0,-6, 0,-6,0,-7,0,11,0,-27,0,-17,0,-4,0,-11,0,-27,0,0,0,-13,0,-19,0,11,0,10, 0,-22,0,11,0,-38,0,-6,0,-5,0,-30,0,4,0,-13,0,11,0,-4,0,-7,0] 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: \(11\)
Coefficient field: \(\mathbb{Q}[x]/(x^{11} - \cdots)\)
Copy content comment:defining polynomial
 
Copy content gp:f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{11} - x^{10} - 24x^{9} + 42x^{8} + 144x^{7} - 377x^{6} + 28x^{5} + 456x^{4} - 180x^{3} - 157x^{2} + 61x - 1 \) 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.

\(\operatorname{Tr}(f)(q) = \) \( 11 q + 11 q^{3} + 11 q^{5} - 4 q^{7} + 11 q^{9} - 7 q^{11} - 11 q^{13} + 11 q^{15} - 6 q^{17} + 11 q^{19} - 4 q^{21} + 11 q^{25} + 11 q^{27} - 5 q^{29} - 13 q^{31} - 7 q^{33} - 4 q^{35} - 14 q^{37} - 11 q^{39}+ \cdots - 7 q^{99}+O(q^{100}) \) 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.