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Properties

Label 44436.2.a.bk
Level $44436$
Weight $2$
Character orbit 44436.a
Self dual yes
Analytic conductor $354.823$
Dimension $5$

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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] = [44436,2,Mod(1,44436)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)
 
Copy content sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(44436, base_ring=CyclotomicField(2)) chi = DirichletCharacter(H, H._module([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("44436.1"); S:= CuspForms(chi, 2); N := Newforms(S);
 
Level: \( N \) \(=\) \( 44436 = 2^{2} \cdot 3 \cdot 7 \cdot 23^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 44436.a (trivial)

Newform invariants

Copy content comment:select newform
 
Copy content sage:traces = [5,0,-5,0,-2,0,-5,0,5,0,5,0,-2,0,2,0,4,0,1,0,5,0,0,0,9,0,-5,0, 0,0,4,0,-5,0,2,0,-4,0,2,0,-7,0,16,0,-2,0,-9,0,5,0,-4,0,11,0,-2,0,-1,0, -5,0,1,0,-5,0,-16,0,-2,0,0,0,14,0,10,0,-9,0,-5,0,-20,0,5,0,-14,0,-18,0, 0,0,-12,0,2,0,-4,0,-14,0,-8,0,5,0] 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: \(354.823246422\)
Dimension: \(5\)
Coefficient field: 5.5.14982192.1
Copy content comment:defining polynomial
 
Copy content gp:f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{5} - 2x^{4} - 15x^{3} + 16x^{2} + 19x - 18 \) 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.

\(\operatorname{Tr}(f)(q) = \) \( 5 q - 5 q^{3} - 2 q^{5} - 5 q^{7} + 5 q^{9} + 5 q^{11} - 2 q^{13} + 2 q^{15} + 4 q^{17} + q^{19} + 5 q^{21} + 9 q^{25} - 5 q^{27} + 4 q^{31} - 5 q^{33} + 2 q^{35} - 4 q^{37} + 2 q^{39} - 7 q^{41} + 16 q^{43}+ \cdots + 5 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Atkin-Lehner signs

\( p \) Sign
\(2\) \( -1 \)
\(3\) \( +1 \)
\(7\) \( +1 \)
\(23\) \( -1 \)

Inner twists

Inner twists of this newform have not been computed.

Twists

Twists of this newform have not been computed.