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Properties

Label 16245.2.a.bg
Level $16245$
Weight $2$
Character orbit 16245.a
Self dual yes
Analytic conductor $129.717$
Dimension $3$

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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] = [16245,2,Mod(1,16245)] 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("16245.1"); S:= CuspForms(chi, 2); N := Newforms(S);
 
Copy content sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(16245, base_ring=CyclotomicField(2)) chi = DirichletCharacter(H, H._module([0, 0, 0])) N = Newforms(chi, 2, names="a")
 
Level: \( N \) \(=\) \( 16245 = 3^{2} \cdot 5 \cdot 19^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 16245.a (trivial)

Newform invariants

Copy content comment:select newform
 
Copy content sage:traces = [3,1,0,1,-3,0,0,3,0,-1,8,0,-8,-4,0,-3,-2,0,0,-1,0,16,4,0,3,6, 0,12,-10,0,-4,-3,0,-18,0,0,-20,0,0,-3,-2,0,-4,12,0,-12,0,0,11,1,0,-4,16, 0,-8,16,0,6,-20,0,-2,-28,0,-11,8,0,-2,2,0,4,-4,0,2,2,0,0,-8,0,0,3,0,-18, 32,0,2,-16,0,4,2,0,-20,-8,0,4,0,0,-20,-15,0,1] 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: \(129.716978084\)
Dimension: \(3\)
Coefficient field: 3.3.148.1
Copy content comment:defining polynomial
 
Copy content gp:f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{3} - x^{2} - 3x + 1 \) 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.

\(\operatorname{Tr}(f)(q) = \) \( 3 q + q^{2} + q^{4} - 3 q^{5} + 3 q^{8} - q^{10} + 8 q^{11} - 8 q^{13} - 4 q^{14} - 3 q^{16} - 2 q^{17} - q^{20} + 16 q^{22} + 4 q^{23} + 3 q^{25} + 6 q^{26} + 12 q^{28} - 10 q^{29} - 4 q^{31} - 3 q^{32}+ \cdots - 15 q^{98}+O(q^{100}) \) Copy content Toggle raw display

Atkin-Lehner signs

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

Inner twists

Inner twists of this newform have not been computed.

Twists

Twists of this newform have not been computed.