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Properties

Label 45760.2.a.ed
Level $45760$
Weight $2$
Character orbit 45760.a
Self dual yes
Analytic conductor $365.395$
Dimension $3$

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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 = [3,0,2,0,3,0,-4,0,9,0,3,0,-3,0,2,0,14,0,-4,0,14,0,10,0,3,0,8, 0,4,0,-14,0,2,0,-4,0,-6,0,-2,0,-14,0,18,0,9,0,0,0,1,0,26,0,2,0,3,0,-2, 0,20,0,-12,0,-4,0,-3,0,-8,0,-18,0,-14,0,6,0,2,0,-4,0,22,0,11,0,0,0,14, 0,2,0,14,0,4,0,32,0,-4,0,-20,0,9,0] 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: \(3\)
Coefficient field: 3.3.1708.1
Copy content comment:defining polynomial
 
Copy content gp:f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{3} - x^{2} - 8x - 2 \) 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.

\(\operatorname{Tr}(f)(q) = \) \( 3 q + 2 q^{3} + 3 q^{5} - 4 q^{7} + 9 q^{9} + 3 q^{11} - 3 q^{13} + 2 q^{15} + 14 q^{17} - 4 q^{19} + 14 q^{21} + 10 q^{23} + 3 q^{25} + 8 q^{27} + 4 q^{29} - 14 q^{31} + 2 q^{33} - 4 q^{35} - 6 q^{37}+ \cdots + 9 q^{99}+O(q^{100}) \) 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.