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Properties

Label 12482.2.a.g
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 = [1,1,0,1,0,0,3,1,-3,0,-2,0,-2,3,0,1,3,-3,0,0,0,-2,1,0,-5,-2,0, 3,-6,0,-4,1,0,3,0,-3,4,0,0,0,7,0,8,-2,0,1,0,0,2,-5,0,-2,-12,0,0,3,0,-6, -14,0,-6,-4,-9,1,0,0,-2,3,0,0,-9,-3,3,4,0,0,-6,0,0,0,9,7,2,0,0,8,0,-2, -1,0,-6,1,0,0,0,0,-14,2,6,-5] 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)
 
\(f(q)\) \(=\) \( q + q^{2} + q^{4} + 3 q^{7} + q^{8} - 3 q^{9} - 2 q^{11} - 2 q^{13} + 3 q^{14} + q^{16} + 3 q^{17} - 3 q^{18} - 2 q^{22} + q^{23} - 5 q^{25} - 2 q^{26} + 3 q^{28} - 6 q^{29} - 4 q^{31} + q^{32} + 3 q^{34}+ \cdots + 6 q^{99}+O(q^{100}) \) 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.