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Properties

Label 10005.2.a.k
Level $10005$
Weight $2$
Character orbit 10005.a
Self dual yes
Analytic conductor $79.890$
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] = [10005,2,Mod(1,10005)] 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("10005.1"); S:= CuspForms(chi, 2); N := Newforms(S);
 
Copy content sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(10005, base_ring=CyclotomicField(2)) chi = DirichletCharacter(H, H._module([0, 0, 0, 0])) N = Newforms(chi, 2, names="a")
 
Level: \( N \) \(=\) \( 10005 = 3 \cdot 5 \cdot 23 \cdot 29 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 10005.a (trivial)

Newform invariants

Copy content comment:select newform
 
Copy content sage:traces = [1,1,-1,-1,1,-1,0,-3,1,1,4,1,-2,0,-1,-1,-6,1,4,-1,0,4,-1,3,1, -2,-1,0,1,-1,4,5,-4,-6,0,-1,-2,4,2,-3,-6,0,0,-4,1,-1,0,1,-7,1,6,2,-10, -1,4,0,-4,1,12,1,-6,4,0,7,-2,-4,4,6,1,0,0,-3,-10,-2,-1,-4,0,2,8,-1,1,-6, 12,0,-6,0,-1,-12,6,1,0,1,-4,0,4,-5,-6,-7,4,-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: \(79.8903272223\)
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)
 
\(f(q)\) \(=\) \( q + q^{2} - q^{3} - q^{4} + q^{5} - q^{6} - 3 q^{8} + q^{9} + q^{10} + 4 q^{11} + q^{12} - 2 q^{13} - q^{15} - q^{16} - 6 q^{17} + q^{18} + 4 q^{19} - q^{20} + 4 q^{22} - q^{23} + 3 q^{24}+ \cdots + 4 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Atkin-Lehner signs

\( p \) Sign
\(3\) \( +1 \)
\(5\) \( -1 \)
\(23\) \( +1 \)
\(29\) \( -1 \)

Inner twists

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

Twists

Twists of this newform have not been computed.