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Properties

Label 18032.2.a.cp
Level $18032$
Weight $2$
Character orbit 18032.a
Self dual yes
Analytic conductor $143.986$
Dimension $4$

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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] = [18032,2,Mod(1,18032)] 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("18032.1"); S:= CuspForms(chi, 2); N := Newforms(S);
 
Copy content sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(18032, base_ring=CyclotomicField(2)) chi = DirichletCharacter(H, H._module([0, 0, 0, 0])) N = Newforms(chi, 2, names="a")
 
Level: \( N \) \(=\) \( 18032 = 2^{4} \cdot 7^{2} \cdot 23 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 18032.a (trivial)

Newform invariants

Copy content comment:select newform
 
Copy content sage:traces = [4,0,1,0,-3,0,0,0,7,0,6,0,1,0,-3,0,-15,0,-1,0,0,0,-4,0,-5,0,-5, 0,6,0,8,0,-9,0,0,0,8,0,25,0,-9,0,-14,0,-21,0,9,0,0,0,-6,0,-3,0,-12,0,23, 0,12,0,-11,0,0,0,0,0,1,0,-1,0,3,0,4,0,22,0,0,0,-5,0,-8,0,12,0,24,0,-9, 0,-27,0,0,0,-25,0,3,0,-2,0,9,0] 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: \(143.986244925\)
Dimension: \(4\)
Coefficient field: 4.4.14013.1
Copy content comment:defining polynomial
 
Copy content gp:f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{4} - x^{3} - 6x^{2} + 6x + 3 \) 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.

\(\operatorname{Tr}(f)(q) = \) \( 4 q + q^{3} - 3 q^{5} + 7 q^{9} + 6 q^{11} + q^{13} - 3 q^{15} - 15 q^{17} - q^{19} - 4 q^{23} - 5 q^{25} - 5 q^{27} + 6 q^{29} + 8 q^{31} - 9 q^{33} + 8 q^{37} + 25 q^{39} - 9 q^{41} - 14 q^{43} - 21 q^{45}+ \cdots + 9 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Atkin-Lehner signs

\( p \) Sign
\(2\) \( -1 \)
\(7\) \( -1 \)
\(23\) \( +1 \)

Inner twists

Inner twists of this newform have not been computed.

Twists

Twists of this newform have not been computed.