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Properties

Label 32490.2.a.cf
Level $32490$
Weight $2$
Character orbit 32490.a
Self dual yes
Analytic conductor $259.434$
Dimension $2$

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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 = [2,-2,0,2,-2,0,-2,-2,0,2,1,0,1,2,0,2,0,0,0,-2,0,-1,-1,0,2,-1, 0,-2,-12,0,3,-2,0,0,2,0,2,0,0,2,1,0,9,1,0,1,0,0,-12,-2,0,1,11,0,-1,2,0, 12,-10,0,-3,-3,0,2,-1,0,13,0,0,-2,2,0,-15,-2,0,0,-1,0,5,-2,0,-1,-12,0, 0,-9,0,-1,9,0,-1,-1,0,0,0,0,20,12,0,2] 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: \(2\)
Coefficient field: \(\Q(\sqrt{73}) \)
Copy content comment:defining polynomial
 
Copy content gp:f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{2} - x - 18 \) Copy content Toggle raw display
Twist minimal: not computed
Fricke sign: \(+1\)
Sato-Tate group: $\mathrm{SU}(2)$

$q$-expansion

The algebraic \(q\)-expansion of this newform has not been computed, but we have computed the trace expansion.

\(\operatorname{Tr}(f)(q) = \) \( 2 q - 2 q^{2} + 2 q^{4} - 2 q^{5} - 2 q^{7} - 2 q^{8} + 2 q^{10} + q^{11} + q^{13} + 2 q^{14} + 2 q^{16} - 2 q^{20} - q^{22} - q^{23} + 2 q^{25} - q^{26} - 2 q^{28} - 12 q^{29} + 3 q^{31} - 2 q^{32}+ \cdots + 12 q^{98}+O(q^{100}) \) 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.