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Properties

Label 12996.2.a.h
Level $12996$
Weight $2$
Character orbit 12996.a
Self dual yes
Analytic conductor $103.774$
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] = [12996,2,Mod(1,12996)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)
 
Copy content sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(12996, base_ring=CyclotomicField(2)) chi = DirichletCharacter(H, H._module([0, 0, 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("12996.1"); S:= CuspForms(chi, 2); N := Newforms(S);
 
Level: \( N \) \(=\) \( 12996 = 2^{2} \cdot 3^{2} \cdot 19^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 12996.a (trivial)

Newform invariants

Copy content comment:select newform
 
Copy content sage:traces = [1,0,0,0,0,0,5,0,0,0,0,0,5,0,0,0,0,0,0,0,0,0,0,0,-5,0,0,0,0,0, -7,0,0,0,0,0,11,0,0,0,0,0,-13,0,0,0,0,0,18,0,0,0,0,0,0,0,0,0,0,0,-1,0, 0,0,0,0,11,0,0,0,0,0,17,0,0,0,0,0,17,0,0,0,0,0,0,0,0,0,0,0,25,0,0,0,0, 0,14,0,0,0] 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: \(103.773582467\)
Dimension: \(1\)
Coefficient field: \(\mathbb{Q}\)
Coefficient ring: \(\mathbb{Z}\)
Coefficient ring index: \( 1 \)
Twist minimal: not computed
Fricke sign: \(-1\)
Sato-Tate group: not computed

$q$-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)
 
\(f(q)\) \(=\) \( q + 5 q^{7} + 5 q^{13} - 5 q^{25} - 7 q^{31} + 11 q^{37} - 13 q^{43} + 18 q^{49} - q^{61} + 11 q^{67} + 17 q^{73} + 17 q^{79} + 25 q^{91} + 14 q^{97}+O(q^{100}) \) Copy content Toggle raw display

Atkin-Lehner signs

\( p \) Sign
\(2\) \( -1 \)
\(3\) \( +1 \)
\(19\) \( +1 \)

Inner twists

Inner twists of this newform have not been computed.

Twists

Twists of this newform have not been computed.