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Properties

Label 15730.2.a.dh
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,-2,2,10,8,-10,0,-2,-10,2,2,10,-5,8,-6,-10,-7, 0,3,-2,10,-10,-20,2,-13,2,10,10,0,-5,-2,8,-10,-6,2,-10,-21,-7,3,0,-8,3, 16,-2,8,10,-27,-10,-2,-20,0,2,11,-13,-17,2,-26,10,6,10,10,0,-30,-5,-23, -2,35,8,14,-10,-2,-6,0,2,-9,-10,-22,-21,-77,-7,5,3,-9,0,6,-8,-2,3,37,16, 6,-2,-17,8,0,10] 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: \( x^{10} - 2x^{9} - 17x^{8} + 26x^{7} + 107x^{6} - 110x^{5} - 286x^{4} + 172x^{3} + 253x^{2} - 108x - 16 \) 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.

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