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Properties

Label 45738.2.a.ic
Level $45738$
Weight $2$
Character orbit 45738.a
Self dual yes
Analytic conductor $365.220$
Dimension $10$

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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 = [10,-10,0,10,3,0,10,-10,0,-3,0,0,-4,-10,0,10,1,0,-4,3,0,0,17, 0,-5,4,0,10,-5,0,-4,-10,0,-1,3,0,-12,4,0,-3,8,0,-14,0,0,-17,13,0,10,5, 0,-4,22,0,0,-10,0,5,-21,0,-13,4,0,10,-6,0,6,1,0,-3,10,0,-22,12,0,-4,0, 0,-38,3,0,-8,1,0,9,14,0,0,21,0,-4,17,0,-13,-31,0,-13,-10,0,-5] 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: \(10\)
Coefficient field: \(\mathbb{Q}[x]/(x^{10} - \cdots)\)
Copy content comment:defining polynomial
 
Copy content gp:f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{10} - 3x^{9} - 18x^{8} + 45x^{7} + 111x^{6} - 225x^{5} - 247x^{4} + 446x^{3} + 116x^{2} - 265x + 55 \) 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.

\(\operatorname{Tr}(f)(q) = \) \( 10 q - 10 q^{2} + 10 q^{4} + 3 q^{5} + 10 q^{7} - 10 q^{8} - 3 q^{10} - 4 q^{13} - 10 q^{14} + 10 q^{16} + q^{17} - 4 q^{19} + 3 q^{20} + 17 q^{23} - 5 q^{25} + 4 q^{26} + 10 q^{28} - 5 q^{29} - 4 q^{31}+ \cdots - 10 q^{98}+O(q^{100}) \) 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.