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Properties

Label 32490.2.a.cb
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 = [1,1,0,1,1,0,2,1,0,1,6,0,4,2,0,1,-6,0,0,1,0,6,0,0,1,4,0,2,6,0, 4,1,0,-6,2,0,-8,0,0,1,0,0,8,6,0,0,0,0,-3,1,0,4,6,0,6,2,0,6,-6,0,2,4,0, 1,4,0,4,-6,0,2,12,0,-10,-8,0,0,12,0,4,1,0,0,12,0,-6,8,0,6,-12,0,8,0,0, 0,0,0,-2,-3,0,1] 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)
 
\(f(q)\) \(=\) \( q + q^{2} + q^{4} + q^{5} + 2 q^{7} + q^{8} + q^{10} + 6 q^{11} + 4 q^{13} + 2 q^{14} + q^{16} - 6 q^{17} + q^{20} + 6 q^{22} + q^{25} + 4 q^{26} + 2 q^{28} + 6 q^{29} + 4 q^{31} + q^{32} - 6 q^{34}+ \cdots - 3 q^{98}+O(q^{100}) \) 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.