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Properties

Label 19110.2.a.bb
Level $19110$
Weight $2$
Character orbit 19110.a
Self dual yes
Analytic conductor $152.594$
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] = [19110,2,Mod(1,19110)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)
 
Copy content sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(19110, base_ring=CyclotomicField(2)) chi = DirichletCharacter(H, H._module([0, 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("19110.1"); S:= CuspForms(chi, 2); N := Newforms(S);
 
Level: \( N \) \(=\) \( 19110 = 2 \cdot 3 \cdot 5 \cdot 7^{2} \cdot 13 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 19110.a (trivial)

Newform invariants

Copy content comment:select newform
 
Copy content sage:traces = [1,-1,1,1,-1,-1,0,-1,1,1,2,1,-1,0,-1,1,-6,-1,-2,-1,0,-2,4,-1, 1,1,1,0,-4,1,0,-1,2,6,0,1,-2,2,-1,1,6,0,0,2,-1,-4,-8,1,0,-1,-6,-1,10,-1, -2,0,-2,4,8,-1,-4,0,0,1,1,-2,2,-6,4,0,8,-1,14,2,1,-2,0,1,-8,-1,1,-6,-14, 0,6,0,-4,-2,6,1,0,4,0,8,2,-1,-6,0,2,1] 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: \(152.594118263\)
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)
 
\(f(q)\) \(=\) \( q - q^{2} + q^{3} + q^{4} - q^{5} - q^{6} - q^{8} + q^{9} + q^{10} + 2 q^{11} + q^{12} - q^{13} - q^{15} + q^{16} - 6 q^{17} - q^{18} - 2 q^{19} - q^{20} - 2 q^{22} + 4 q^{23} - q^{24} + q^{25}+ \cdots + 2 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Atkin-Lehner signs

\( p \) Sign
\(2\) \( +1 \)
\(3\) \( -1 \)
\(5\) \( +1 \)
\(7\) \( -1 \)
\(13\) \( +1 \)

Inner twists

Inner twists of this newform have not been computed.

Twists

Twists of this newform have not been computed.