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Properties

Label 15730.2.a.cn
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 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);
 
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")
 
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,-3,5,5,-3,3,5,4,5,0,-3,-5,3,-3,5,-1,4,3,5,-1,0,-4,-3,5,-5, -27,3,-9,-3,-9,5,0,-1,3,4,-7,3,3,5,-10,-1,-14,0,4,-4,-16,-3,0,5,-35,-5, -9,-27,0,3,-1,-9,-10,-3,-9,-9,-8,5,-5,0,-20,-1,-32,3,5,4,-38,-7,-3,3,0, 3,14,5,37,-10,8,-1,-1,-14,19,0,-21,4,-3,-4,3,-16,3,-3,4,0,0,5] 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: 5.5.1095904.1
Copy content comment:defining polynomial
 
Copy content gp:f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{5} - 2x^{4} - 7x^{3} + 14x^{2} + 6x - 14 \) 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.

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