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Properties

Label 15730.2.a.bt
Level $15730$
Weight $2$
Character orbit 15730.a
Self dual yes
Analytic conductor $125.605$
Dimension $3$

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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] = [15730,2,Mod(1,15730)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)
 
Copy content sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(15730, 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("15730.1"); S:= CuspForms(chi, 2); N := Newforms(S);
 
Level: \( N \) \(=\) \( 15730 = 2 \cdot 5 \cdot 11^{2} \cdot 13 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 15730.a (trivial)

Newform invariants

Copy content comment:select newform
 
Copy content sage:traces = [3,-3,1,3,-3,-1,2,-3,8,3,0,1,3,-2,-1,3,-3,-8,5,-3,-13,0,0,-1, 3,-3,-14,2,4,1,-17,-3,0,3,-2,8,0,-5,1,3,13,13,10,0,-8,0,-17,1,1,-3,-4, 3,-1,14,0,-2,29,-4,-6,-1,11,17,26,3,-3,0,9,-3,-9,2,-1,-8,9,0,1,5,0,-1, -5,-3,-9,-13,-1,-13,3,-10,-23,0,-13,8,2,0,17,17,-5,-1,2,-1,0,3] 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: \(125.604682379\)
Dimension: \(3\)
Coefficient field: 3.3.473.1
Copy content comment:defining polynomial
 
Copy content gp:f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{3} - 5x - 1 \) 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.

\(\operatorname{Tr}(f)(q) = \) \( 3 q - 3 q^{2} + q^{3} + 3 q^{4} - 3 q^{5} - q^{6} + 2 q^{7} - 3 q^{8} + 8 q^{9} + 3 q^{10} + q^{12} + 3 q^{13} - 2 q^{14} - q^{15} + 3 q^{16} - 3 q^{17} - 8 q^{18} + 5 q^{19} - 3 q^{20} - 13 q^{21}+ \cdots - q^{98}+O(q^{100}) \) Copy content Toggle raw display

Atkin-Lehner signs

\( p \) Sign
\(2\) \( +1 \)
\(5\) \( +1 \)
\(11\) \( -1 \)
\(13\) \( -1 \)

Inner twists

Inner twists of this newform have not been computed.

Twists

Twists of this newform have not been computed.