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Properties

Label 10230.2.a.k
Level $10230$
Weight $2$
Character orbit 10230.a
Self dual yes
Analytic conductor $81.687$
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] = [10230,2,Mod(1,10230)] 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("10230.1"); S:= CuspForms(chi, 2); N := Newforms(S);
 
Copy content sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(10230, base_ring=CyclotomicField(2)) chi = DirichletCharacter(H, H._module([0, 0, 0, 0])) N = Newforms(chi, 2, names="a")
 
Level: \( N \) \(=\) \( 10230 = 2 \cdot 3 \cdot 5 \cdot 11 \cdot 31 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 10230.a (trivial)

Newform invariants

Copy content comment:select newform
 
Copy content sage:traces = [1,-1,-1,1,1,1,3,-1,1,-1,-1,-1,-2,-3,-1,1,-7,-1,8,1,-3,1,7,1, 1,2,-1,3,2,1,-1,-1,1,7,3,1,-9,-8,2,-1,-10,3,11,-1,1,-7,6,-1,2,-1,7,-2, 10,1,-1,-3,-8,-2,-9,-1,-8,1,3,1,-2,-1,5,-7,-7,-3,-6,-1,6,9,-1,8,-3,-2, 8,1,1,10,9,-3,-7,-11,-2,1,12,-1,-6,7,1,-6,8,1,11,-2,-1,1] 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: \(81.6869612678\)
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)
 
\(f(q)\) \(=\) \( q - q^{2} - q^{3} + q^{4} + q^{5} + q^{6} + 3 q^{7} - q^{8} + q^{9} - q^{10} - q^{11} - q^{12} - 2 q^{13} - 3 q^{14} - q^{15} + q^{16} - 7 q^{17} - q^{18} + 8 q^{19} + q^{20} - 3 q^{21} + q^{22}+ \cdots - q^{99}+O(q^{100}) \) Copy content Toggle raw display

Atkin-Lehner signs

\( p \) Sign
\(2\) \( +1 \)
\(3\) \( +1 \)
\(5\) \( -1 \)
\(11\) \( +1 \)
\(31\) \( +1 \)

Inner twists

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

Twists

Twists of this newform have not been computed.