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Properties

Label 17784.2.a.bp
Level $17784$
Weight $2$
Character orbit 17784.a
Self dual yes
Analytic conductor $142.006$
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] = [17784,2,Mod(1,17784)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)
 
Copy content sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(17784, base_ring=CyclotomicField(2)) chi = DirichletCharacter(H, H._module([0, 0, 0, 0, 0])) N = Newforms(chi, 2, names="a")
 
Copy content magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("17784.1"); S:= CuspForms(chi, 2); N := Newforms(S);
 
Level: \( N \) \(=\) \( 17784 = 2^{3} \cdot 3^{2} \cdot 13 \cdot 19 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 17784.a (trivial)

Newform invariants

Copy content comment:select newform
 
Copy content sage:traces = [4,0,0,0,4,0,-4,0,0,0,2,0,4,0,0,0,2,0,4,0,0,0,-6,0,-8,0,0,0,4, 0,-12,0,0,0,-8,0,2,0,0,0,-16,0,-10,0,0,0,-2,0,28,0,0,0,26,0,-10,0,0,0, -10,0,16,0,0,0,4,0,16,0,0,0,10,0,14,0,0,0,-14,0,-10,0,0,0,4,0,10,0,0,0, 40,0,-4,0,0,0,4,0,-18,0,0,0] 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: \(142.005954955\)
Dimension: \(4\)
Coefficient field: 4.4.7232.1
Copy content comment:defining polynomial
 
Copy content gp:f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{4} - 2x^{3} - 5x^{2} + 4x + 4 \) 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.

\(\operatorname{Tr}(f)(q) = \) \( 4 q + 4 q^{5} - 4 q^{7} + 2 q^{11} + 4 q^{13} + 2 q^{17} + 4 q^{19} - 6 q^{23} - 8 q^{25} + 4 q^{29} - 12 q^{31} - 8 q^{35} + 2 q^{37} - 16 q^{41} - 10 q^{43} - 2 q^{47} + 28 q^{49} + 26 q^{53} - 10 q^{55}+ \cdots - 18 q^{97}+O(q^{100}) \) Copy content Toggle raw display

Atkin-Lehner signs

\( p \) Sign
\(2\) \( -1 \)
\(3\) \( +1 \)
\(13\) \( -1 \)
\(19\) \( -1 \)

Inner twists

Inner twists of this newform have not been computed.

Twists

Twists of this newform have not been computed.