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Properties

Label 10470.2.a.a
Level $10470$
Weight $2$
Character orbit 10470.a
Self dual yes
Analytic conductor $83.603$
Dimension $1$
CM no
Inner twists $1$

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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] = [10470,2,Mod(1,10470)] 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("10470.1"); S:= CuspForms(chi, 2); N := Newforms(S);
 
Copy content sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(10470, base_ring=CyclotomicField(2)) chi = DirichletCharacter(H, H._module([0, 0, 0])) N = Newforms(chi, 2, names="a")
 
Level: \( N \) \(=\) \( 10470 = 2 \cdot 3 \cdot 5 \cdot 349 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 10470.a (trivial)

Newform invariants

Copy content comment:select newform
 
Copy content sage:traces = [1,-1,-1,1,1,1,-4,-1,1,-1,-4,-1,-2,4,-1,1,-6,-1,4,1,4,4,0,1,1, 2,-1,-4,6,1,8,-1,4,6,-4,1,-10,-4,2,-1,2,-4,8,-4,1,0,-8,-1,9,-1,6,-2,2, 1,-4,4,-4,-6,12,-1,-2,-8,-4,1,-2,-4,12,-6,0,4,-8,-1,10,10,-1,4,16,-2,4, 1,1,-2,4,4,-6,-8,-6,4,14,-1,8,0,-8,8,4,1,2,-9,-4,1] 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: \(83.6033709163\)
Dimension: \(1\)
Coefficient field: \(\mathbb{Q}\)
Coefficient ring: \(\mathbb{Z}\)
Coefficient ring index: \( 1 \)
Twist minimal: yes
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)
 
\(f(q)\) \(=\) \( q - q^{2} - q^{3} + q^{4} + q^{5} + q^{6} - 4 q^{7} - q^{8} + q^{9} - q^{10} - 4 q^{11} - q^{12} - 2 q^{13} + 4 q^{14} - q^{15} + q^{16} - 6 q^{17} - q^{18} + 4 q^{19} + q^{20} + 4 q^{21}+ \cdots - 4 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Atkin-Lehner signs

\( p \) Sign
\(2\) \( +1 \)
\(3\) \( +1 \)
\(5\) \( -1 \)
\(349\) \( -1 \)

Inner twists

This newform does not admit any (nontrivial) inner twists.

Twists

Twists of this newform have not been computed.