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Properties

Label 45760.2.a.ge
Level $45760$
Weight $2$
Character orbit 45760.a
Self dual yes
Analytic conductor $365.395$
Dimension $13$

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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 = [13,0,-5,0,13,0,-3,0,16,0,-13,0,-13,0,-5,0,10,0,-18,0,-1,0,-8, 0,13,0,-17,0,15,0,-5,0,5,0,-3,0,8,0,5,0,29,0,-27,0,16,0,-17,0,8,0,-27, 0,1,0,-13,0,15,0,-30,0,23,0,22,0,-13,0,-31,0,-6,0,-11,0,14,0,-5,0,3,0, -20,0,29,0,-32,0,10,0,13,0,9,0,3,0,-7,0,-18,0,21,0,-16,0] 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: \(13\)
Coefficient field: \(\mathbb{Q}[x]/(x^{13} - \cdots)\)
Copy content comment:defining polynomial
 
Copy content gp:f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{13} - 5 x^{12} - 15 x^{11} + 101 x^{10} + 37 x^{9} - 685 x^{8} + 240 x^{7} + 1934 x^{6} - 1216 x^{5} + \cdots + 16 \) 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.

\(\operatorname{Tr}(f)(q) = \) \( 13 q - 5 q^{3} + 13 q^{5} - 3 q^{7} + 16 q^{9} - 13 q^{11} - 13 q^{13} - 5 q^{15} + 10 q^{17} - 18 q^{19} - q^{21} - 8 q^{23} + 13 q^{25} - 17 q^{27} + 15 q^{29} - 5 q^{31} + 5 q^{33} - 3 q^{35} + 8 q^{37}+ \cdots - 16 q^{99}+O(q^{100}) \) 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.