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Properties

Label 15730.2.a.cu
Level $15730$
Weight $2$
Character orbit 15730.a
Self dual yes
Analytic conductor $125.605$
Dimension $6$

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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 = [6,-6,3,6,6,-3,-3,-6,9,-6,0,3,-6,3,3,6,-1,-9,-3,6,5,0,10,-3,6, 6,9,-3,-11,-3,3,-6,0,1,-3,9,7,3,-3,-6,-6,-5,14,0,9,-10,18,3,1,-6,-9,-6, 13,-9,0,3,5,11,-2,3,-3,-3,-4,6,-6,0,10,-1,20,3,25,-9,-8,-7,3,-3,0,3,-10, 6,-2,6,-24,5,-1,-14,21,0,9,-9,3,10,-13,-18,-3,-3,6,-1,0,6] 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: \(6\)
Coefficient field: 6.6.705170192.1
Copy content comment:defining polynomial
 
Copy content gp:f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{6} - 3x^{5} - 9x^{4} + 19x^{3} + 26x^{2} - 4x - 2 \) 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.

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