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Properties

Label 10005.2.a.c
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,-4,3,1,-1,6,1,-6,4,-1,-1,0,-1,-4,-1,4,-6,-1,-3, 1,6,-1,4,1,1,10,-5,-6,0,-4,-1,-6,4,6,3,-10,-4,12,-6,1,1,8,1,9,-1,0,6,-6, 1,6,-12,4,-1,-2,1,2,-10,-4,7,-6,6,-12,0,1,4,2,3,4,6,-1,4,-24,-6,0,-1,1, 10,12,-4,0,-12,-1,18,14,-1,24,1,-10,-8,-4,5,-6,-9,6,-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)
 
\(f(q)\) \(=\) \( q - q^{2} - q^{3} - q^{4} + q^{5} + q^{6} - 4 q^{7} + 3 q^{8} + q^{9} - q^{10} + 6 q^{11} + q^{12} - 6 q^{13} + 4 q^{14} - q^{15} - q^{16} - q^{18} - 4 q^{19} - q^{20} + 4 q^{21} - 6 q^{22}+ \cdots + 6 q^{99}+O(q^{100}) \) 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.