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Properties

Label 32490.2.a.r
Level $32490$
Weight $2$
Character orbit 32490.a
Self dual yes
Analytic conductor $259.434$
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] = [32490,2,Mod(1,32490)] 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("32490.1"); S:= CuspForms(chi, 2); N := Newforms(S);
 
Copy content sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(32490, base_ring=CyclotomicField(2)) chi = DirichletCharacter(H, H._module([0, 0, 0])) N = Newforms(chi, 2, names="a")
 
Level: \( N \) \(=\) \( 32490 = 2 \cdot 3^{2} \cdot 5 \cdot 19^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 32490.a (trivial)

Newform invariants

Copy content comment:select newform
 
Copy content sage:traces = [1,-1,0,1,1,0,-1,-1,0,-1,-2,0,-3,1,0,1,-4,0,0,1,0,2,6,0,1,3,0, -1,10,0,1,-1,0,4,-1,0,-5,0,0,-1,-2,0,-5,-2,0,-6,0,0,-6,-1,0,-3,12,0,-2, 1,0,-10,2,0,5,-1,0,1,-3,0,-5,-4,0,1,0,0,11,5,0,0,2,0,-11,1,0,2,-2,0,-4, 5,0,2,0,0,3,6,0,0,0,0,-2,6,0,1] 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: \(259.433956167\)
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)
 
\(f(q)\) \(=\) \( q - q^{2} + q^{4} + q^{5} - q^{7} - q^{8} - q^{10} - 2 q^{11} - 3 q^{13} + q^{14} + q^{16} - 4 q^{17} + q^{20} + 2 q^{22} + 6 q^{23} + q^{25} + 3 q^{26} - q^{28} + 10 q^{29} + q^{31} - q^{32}+ \cdots + 6 q^{98}+O(q^{100}) \) Copy content Toggle raw display

Atkin-Lehner signs

\( p \) Sign
\(2\) \( +1 \)
\(3\) \( -1 \)
\(5\) \( -1 \)
\(19\) \( +1 \)

Inner twists

Inner twists of this newform have not been computed.

Twists

Twists of this newform have not been computed.