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Properties

Label 45738.2.a.he
Level $45738$
Weight $2$
Character orbit 45738.a
Self dual yes
Analytic conductor $365.220$
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] = [45738,2,Mod(1,45738)] 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("45738.1"); S:= CuspForms(chi, 2); N := Newforms(S);
 
Copy content sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(45738, base_ring=CyclotomicField(2)) chi = DirichletCharacter(H, H._module([0, 0, 0])) N = Newforms(chi, 2, names="a")
 
Level: \( N \) \(=\) \( 45738 = 2 \cdot 3^{3} \cdot 7 \cdot 11^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 45738.a (trivial)

Newform invariants

Copy content comment:select newform
 
Copy content sage:traces = [5,5,0,5,-2,0,-5,5,0,-2,0,0,0,-5,0,5,2,0,-2,-2,0,0,-8,0,11,0, 0,-5,6,0,10,5,0,2,2,0,-4,-2,0,-2,8,0,-7,0,0,-8,-11,0,5,11,0,0,-19,0,0, -5,0,6,-18,0,0,10,0,5,-8,0,4,2,0,2,-8,0,-11,-4,0,-2,0,0,0,-2,0,8,11,0, -28,-7,0,0,-19,0,0,-8,0,-11,-14,0,6,5,0,11] 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: \(365.219768765\)
Dimension: \(5\)
Coefficient field: 5.5.1021221.1
Copy content comment:defining polynomial
 
Copy content gp:f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{5} - x^{4} - 10x^{3} - 7x^{2} + 4x + 1 \) 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.

\(\operatorname{Tr}(f)(q) = \) \( 5 q + 5 q^{2} + 5 q^{4} - 2 q^{5} - 5 q^{7} + 5 q^{8} - 2 q^{10} - 5 q^{14} + 5 q^{16} + 2 q^{17} - 2 q^{19} - 2 q^{20} - 8 q^{23} + 11 q^{25} - 5 q^{28} + 6 q^{29} + 10 q^{31} + 5 q^{32} + 2 q^{34} + 2 q^{35}+ \cdots + 5 q^{98}+O(q^{100}) \) Copy content Toggle raw display

Atkin-Lehner signs

\( p \) Sign
\(2\) \( -1 \)
\(3\) \( -1 \)
\(7\) \( +1 \)
\(11\) \( +1 \)

Inner twists

Inner twists of this newform have not been computed.

Twists

Twists of this newform have not been computed.