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Properties

Label 15730.2.a.df
Level $15730$
Weight $2$
Character orbit 15730.a
Self dual yes
Analytic conductor $125.605$
Dimension $10$

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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 = [10,-10,2,10,-10,-2,-2,-10,10,10,0,2,10,2,-2,10,-4,-10,2,-10, -4,0,2,-2,10,-10,14,-2,8,2,12,-10,0,4,2,10,-4,-2,2,10,8,4,-16,0,-10,-2, 18,2,-6,-10,10,10,28,-14,0,2,22,-8,42,-2,-32,-12,-2,10,-10,0,-4,-4,-14, -2,20,-10,0,4,2,2,0,-2,-6,-10,-2,-8,-20,-4,4,16,-44,0,40,10,-2,2,-12,-18, -2,-2,20,6,0,10] 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: \(10\)
Coefficient field: \(\mathbb{Q}[x]/(x^{10} - \cdots)\)
Copy content comment:defining polynomial
 
Copy content gp:f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{10} - 2x^{9} - 18x^{8} + 30x^{7} + 111x^{6} - 132x^{5} - 273x^{4} + 174x^{3} + 177x^{2} - 56x + 4 \) 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.

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