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Properties

Label 15730.2.a.dr
Level $15730$
Weight $2$
Character orbit 15730.a
Self dual yes
Analytic conductor $125.605$
Dimension $16$

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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 = [16,-16,1,16,16,-1,-8,-16,23,-16,0,1,-16,8,1,16,-20,-23,-7,16, -5,0,-9,-1,16,16,4,-8,-19,-1,-12,-16,0,20,-8,23,6,7,-1,-16,-28,5,-16,0, 23,9,-8,1,54,-16,5,-16,-12,-4,0,8,7,19,16,1,-24,12,-70,16,-16,0,25,-20, 7,8,27,-23,-17,-6,1,-7,0,1,-3,16,12,28,-42,-5,-20,16,-49,0,23,-23,8,-9, 55,8,-7,-1,20,-54,0,16] 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: \(16\)
Coefficient field: \(\mathbb{Q}[x]/(x^{16} - \cdots)\)
Copy content comment:defining polynomial
 
Copy content gp:f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{16} - x^{15} - 35 x^{14} + 32 x^{13} + 489 x^{12} - 381 x^{11} - 3517 x^{10} + 2082 x^{9} + \cdots + 400 \) 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.

\(\operatorname{Tr}(f)(q) = \) \( 16 q - 16 q^{2} + q^{3} + 16 q^{4} + 16 q^{5} - q^{6} - 8 q^{7} - 16 q^{8} + 23 q^{9} - 16 q^{10} + q^{12} - 16 q^{13} + 8 q^{14} + q^{15} + 16 q^{16} - 20 q^{17} - 23 q^{18} - 7 q^{19} + 16 q^{20}+ \cdots - 54 q^{98}+O(q^{100}) \) 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.