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Properties

Label 39710.2.a.s
Level $39710$
Weight $2$
Character orbit 39710.a
Self dual yes
Analytic conductor $317.086$
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] = [39710,2,Mod(1,39710)] 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("39710.1"); S:= CuspForms(chi, 2); N := Newforms(S);
 
Copy content sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(39710, base_ring=CyclotomicField(2)) chi = DirichletCharacter(H, H._module([0, 0, 0])) N = Newforms(chi, 2, names="a")
 
Level: \( N \) \(=\) \( 39710 = 2 \cdot 5 \cdot 11 \cdot 19^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 39710.a (trivial)

Newform invariants

Copy content comment:select newform
 
Copy content sage:traces = [1,1,-1,1,-1,-1,4,1,-2,-1,-1,-1,-3,4,1,1,6,-2,0,-1,-4,-1,3,-1, 1,-3,5,4,-4,1,5,1,1,6,-4,-2,8,0,3,-1,3,-4,7,-1,2,3,-7,-1,9,1,-6,-3,0,5, 1,4,0,-4,10,1,3,5,-8,1,3,1,13,6,-3,-4,-12,-2,-3,8,-1,0,-4,3,8,-1,1,3,-7, -4,-6,7,4,-1,2,2,-12,3,-5,-7,0,-1,2,9,2,1] 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: \(317.085946427\)
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)
 
\(f(q)\) \(=\) \( q + q^{2} - q^{3} + q^{4} - q^{5} - q^{6} + 4 q^{7} + q^{8} - 2 q^{9} - q^{10} - q^{11} - q^{12} - 3 q^{13} + 4 q^{14} + q^{15} + q^{16} + 6 q^{17} - 2 q^{18} - q^{20} - 4 q^{21} - q^{22}+ \cdots + 2 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Atkin-Lehner signs

\( p \) Sign
\(2\) \( -1 \)
\(5\) \( +1 \)
\(11\) \( +1 \)
\(19\) \( +1 \)

Inner twists

Inner twists of this newform have not been computed.

Twists

Twists of this newform have not been computed.