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Properties

Label 15730.2.a.bw
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,-1,3,4,-3,0,-1,3,-1,1,3,5,4,-13,-3,3,0,-2,-1, 3,3,-1,-1,5,1,9,3,0,5,1,4,5,-13,-1,-3,-4,3,0,0,-4,-2,-4,-1,4,3,1,3,7,-1, 0,-1,7,5,2,1,-21,9,-26,3,-3,0,8,5,26,1,11,4,6,5,-1,-13,0,-1,-2,-3,-9,-4, -2,3,-5,0,11,0,9,-4,-1,-2,25,-4,13,-1,22,4,0,3] 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: 3.3.229.1
Copy content comment:defining polynomial
 
Copy content gp:f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{3} - 4x - 1 \) 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.

\(\operatorname{Tr}(f)(q) = \) \( 3 q + 3 q^{2} - q^{3} + 3 q^{4} - 3 q^{5} - q^{6} - q^{7} + 3 q^{8} + 4 q^{9} - 3 q^{10} - q^{12} + 3 q^{13} - q^{14} + q^{15} + 3 q^{16} + 5 q^{17} + 4 q^{18} - 13 q^{19} - 3 q^{20} + 3 q^{21} - 2 q^{23}+ \cdots + 4 q^{98}+O(q^{100}) \) 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.