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Properties

Label 15730.2.a.o
Level $15730$
Weight $2$
Character orbit 15730.a
Self dual yes
Analytic conductor $125.605$
Dimension $1$

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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 = [1,-1,2,1,1,-2,-4,-1,1,-1,0,2,-1,4,2,1,2,-1,0,1,-8,0,-4,-2,1, 1,-4,-4,8,-2,0,-1,0,-2,-4,1,6,0,-2,-1,8,8,-4,0,1,4,-6,2,9,-1,4,-1,-4,4, 0,4,0,-8,4,2,-8,0,-4,1,-1,0,-12,2,-8,4,16,-1,2,-6,2,0,0,2,12,1,-11,-8, 4,-8,2,4,16,0,6,-1,4,-4,0,6,0,-2,12,-9,0,1] 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: \(1\)
Coefficient field: \(\mathbb{Q}\)
Coefficient ring: \(\mathbb{Z}\)
Coefficient ring index: \( 1 \)
Twist minimal: not computed
Fricke sign: \(+1\)
Sato-Tate group: $\mathrm{SU}(2)$

$q$-expansion

Copy content comment:q-expansion
 
Copy content sage:f.q_expansion() # note that sage often uses an isomorphic number field
 
Copy content gp:mfcoefs(f, 20)
 
\(f(q)\) \(=\) \( q - q^{2} + 2 q^{3} + q^{4} + q^{5} - 2 q^{6} - 4 q^{7} - q^{8} + q^{9} - q^{10} + 2 q^{12} - q^{13} + 4 q^{14} + 2 q^{15} + q^{16} + 2 q^{17} - q^{18} + q^{20} - 8 q^{21} - 4 q^{23} - 2 q^{24}+ \cdots - 9 q^{98}+O(q^{100}) \) 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.