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Properties

Label 45760.2.a.ex
Level $45760$
Weight $2$
Character orbit 45760.a
Self dual yes
Analytic conductor $365.395$
Dimension $6$

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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] = [45760,2,Mod(1,45760)] 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("45760.1"); S:= CuspForms(chi, 2); N := Newforms(S);
 
Copy content sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(45760, base_ring=CyclotomicField(2)) chi = DirichletCharacter(H, H._module([0, 0, 0, 0, 0])) N = Newforms(chi, 2, names="a")
 
Level: \( N \) \(=\) \( 45760 = 2^{6} \cdot 5 \cdot 11 \cdot 13 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 45760.a (trivial)

Newform invariants

Copy content comment:select newform
 
Copy content sage:traces = [6,0,-3,0,6,0,-1,0,9,0,6,0,6,0,-3,0,5,0,-2,0,-2,0,13,0,6,0,-12, 0,-2,0,-4,0,-3,0,-1,0,-1,0,-3,0,8,0,-23,0,9,0,25,0,17,0,-22,0,-5,0,6,0, -5,0,-18,0,10,0,6,0,6,0,-7,0,-16,0,14,0,5,0,-3,0,-1,0,-10,0,34,0,-5,0, 5,0,64,0,4,0,-1,0,-36,0,-2,0,13,0,9,0] 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: \(365.395439649\)
Dimension: \(6\)
Coefficient field: 6.6.573753220.1
Copy content comment:defining polynomial
 
Copy content gp:f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{6} - 3x^{5} - 9x^{4} + 20x^{3} + 17x^{2} - 35x + 5 \) 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.

\(\operatorname{Tr}(f)(q) = \) \( 6 q - 3 q^{3} + 6 q^{5} - q^{7} + 9 q^{9} + 6 q^{11} + 6 q^{13} - 3 q^{15} + 5 q^{17} - 2 q^{19} - 2 q^{21} + 13 q^{23} + 6 q^{25} - 12 q^{27} - 2 q^{29} - 4 q^{31} - 3 q^{33} - q^{35} - q^{37} - 3 q^{39}+ \cdots + 9 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Atkin-Lehner signs

\( p \) Sign
\(2\) \( +1 \)
\(5\) \( -1 \)
\(11\) \( -1 \)
\(13\) \( -1 \)

Inner twists

Inner twists of this newform have not been computed.

Twists

Twists of this newform have not been computed.