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Properties

Label 17550.2.a.ee
Level $17550$
Weight $2$
Character orbit 17550.a
Self dual yes
Analytic conductor $140.137$
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] = [17550,2,Mod(1,17550)] 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("17550.1"); S:= CuspForms(chi, 2); N := Newforms(S);
 
Copy content sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(17550, base_ring=CyclotomicField(2)) chi = DirichletCharacter(H, H._module([0, 0, 0])) N = Newforms(chi, 2, names="a")
 
Level: \( N \) \(=\) \( 17550 = 2 \cdot 3^{3} \cdot 5^{2} \cdot 13 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 17550.a (trivial)

Newform invariants

Copy content comment:select newform
 
Copy content sage:traces = [3,-3,0,3,0,0,-2,-3,0,0,2,0,3,2,0,3,0,0,-8,0,0,-2,2,0,0,-3,0, -2,-10,0,-2,-3,0,0,0,0,-7,8,0,0,2,0,8,2,0,-2,12,0,-9,0,0,3,15,0,0,2,0, 10,8,0,-24,2,0,3,0,0,1,0,0,0,9,0,16,7,0,-8,20,0,-7,0,0,-2,8,0,0,-8,0,-2, -17,0,-2,2,0,-12,0,0,2,9,0,0] 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: \(140.137455547\)
Dimension: \(3\)
Coefficient field: 3.3.564.1
Copy content comment:defining polynomial
 
Copy content gp:f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{3} - x^{2} - 5x + 3 \) 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.

\(\operatorname{Tr}(f)(q) = \) \( 3 q - 3 q^{2} + 3 q^{4} - 2 q^{7} - 3 q^{8} + 2 q^{11} + 3 q^{13} + 2 q^{14} + 3 q^{16} - 8 q^{19} - 2 q^{22} + 2 q^{23} - 3 q^{26} - 2 q^{28} - 10 q^{29} - 2 q^{31} - 3 q^{32} - 7 q^{37} + 8 q^{38} + 2 q^{41}+ \cdots + 9 q^{98}+O(q^{100}) \) Copy content Toggle raw display

Atkin-Lehner signs

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

Inner twists

Inner twists of this newform have not been computed.

Twists

Twists of this newform have not been computed.