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Properties

Label 12482.2.a.b
Level $12482$
Weight $2$
Character orbit 12482.a
Self dual yes
Analytic conductor $99.669$
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] = [12482,2,Mod(1,12482)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)
 
Copy content sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(12482, base_ring=CyclotomicField(2)) chi = DirichletCharacter(H, H._module([0])) N = Newforms(chi, 2, names="a")
 
Copy content magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("12482.1"); S:= CuspForms(chi, 2); N := Newforms(S);
 
Level: \( N \) \(=\) \( 12482 = 2 \cdot 79^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 12482.a (trivial)

Newform invariants

Copy content comment:select newform
 
Copy content sage:traces = [1,-1,0,1,4,0,-1,-1,-3,-4,0,0,-4,1,0,1,-5,3,-6,4,0,0,5,0,11,4, 0,-1,-4,0,-8,-1,0,5,-4,-3,2,6,0,-4,3,0,-4,0,-12,-5,12,0,-6,-11,0,-4,-2, 0,0,1,0,4,12,0,12,8,3,1,-16,0,2,-5,0,4,7,3,3,-2,0,-6,0,0,0,4,9,-3,-2,0, -20,4,0,0,-5,12,4,5,0,-12,-24,0,10,6,0,11] 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: \(99.6692718030\)
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)
 
\(f(q)\) \(=\) \( q - q^{2} + q^{4} + 4 q^{5} - q^{7} - q^{8} - 3 q^{9} - 4 q^{10} - 4 q^{13} + q^{14} + q^{16} - 5 q^{17} + 3 q^{18} - 6 q^{19} + 4 q^{20} + 5 q^{23} + 11 q^{25} + 4 q^{26} - q^{28} - 4 q^{29} - 8 q^{31}+ \cdots + 6 q^{98}+O(q^{100}) \) Copy content Toggle raw display

Atkin-Lehner signs

\( p \) Sign
\(2\) \( +1 \)
\(79\) \( -1 \)

Inner twists

Inner twists of this newform have not been computed.

Twists

Twists of this newform have not been computed.