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Properties

Label 15730.2.a.cl
Level $15730$
Weight $2$
Character orbit 15730.a
Self dual yes
Analytic conductor $125.605$
Dimension $5$

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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 = [5,-5,1,5,-5,-1,5,-5,8,5,0,1,5,-5,-1,5,1,-8,-5,-5,7,0,4,-1,5, -5,7,5,1,1,3,-5,0,-1,-5,8,-5,5,1,5,16,-7,-2,0,-8,-4,6,1,0,-5,-31,5,-37, -7,0,-5,-7,-1,18,-1,-19,-3,56,5,-5,0,-8,1,44,5,13,-8,-18,5,1,-5,0,-1,-18, -5,65,-16,-4,7,-1,2,53,0,23,8,5,4,33,-6,5,-1,-2,0,0,5] 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: \(5\)
Coefficient field: 5.5.4586544.1
Copy content comment:defining polynomial
 
Copy content gp:f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{5} - x^{4} - 11x^{3} + 7x^{2} + 8x - 2 \) 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.

\(\operatorname{Tr}(f)(q) = \) \( 5 q - 5 q^{2} + q^{3} + 5 q^{4} - 5 q^{5} - q^{6} + 5 q^{7} - 5 q^{8} + 8 q^{9} + 5 q^{10} + q^{12} + 5 q^{13} - 5 q^{14} - q^{15} + 5 q^{16} + q^{17} - 8 q^{18} - 5 q^{19} - 5 q^{20} + 7 q^{21} + 4 q^{23}+ \cdots - 2 q^{97}+O(q^{100}) \) 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.