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Properties

Label 22743.2.a.bx
Level $22743$
Weight $2$
Character orbit 22743.a
Self dual yes
Analytic conductor $181.604$
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] = [22743,2,Mod(1,22743)] 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("22743.1"); S:= CuspForms(chi, 2); N := Newforms(S);
 
Copy content sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(22743, base_ring=CyclotomicField(2)) chi = DirichletCharacter(H, H._module([0, 0, 0])) N = Newforms(chi, 2, names="a")
 
Level: \( N \) \(=\) \( 22743 = 3^{2} \cdot 7 \cdot 19^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 22743.a (trivial)

Newform invariants

Copy content comment:select newform
 
Copy content sage:traces = [4,1,0,3,2,0,4,3,0,0,2,0,6,1,0,5,-1,0,0,17,0,16,13,0,4,23,0,3, -3,0,15,12,0,-4,2,0,3,0,0,24,-1,0,-3,15,0,20,23,0,4,17,0,13,7,0,-7,3,0, 1,2,0,-13,-13,0,-19,2,0,16,-41,0,0,13,0,-22,-3,0,0,2,0,15,9,0,-44,37,0, -39,11,0,9,10,0,6,9,0,5,0,0,21,1,0,1] 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: \(181.603769317\)
Dimension: \(4\)
Coefficient field: 4.4.12197.1
Copy content comment:defining polynomial
 
Copy content gp:f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{4} - x^{3} - 5x^{2} + 3x + 1 \) 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.

\(\operatorname{Tr}(f)(q) = \) \( 4 q + q^{2} + 3 q^{4} + 2 q^{5} + 4 q^{7} + 3 q^{8} + 2 q^{11} + 6 q^{13} + q^{14} + 5 q^{16} - q^{17} + 17 q^{20} + 16 q^{22} + 13 q^{23} + 4 q^{25} + 23 q^{26} + 3 q^{28} - 3 q^{29} + 15 q^{31} + 12 q^{32}+ \cdots + q^{98}+O(q^{100}) \) Copy content Toggle raw display

Atkin-Lehner signs

\( p \) Sign
\(3\) \( -1 \)
\(7\) \( -1 \)
\(19\) \( -1 \)

Inner twists

Inner twists of this newform have not been computed.

Twists

Twists of this newform have not been computed.