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Properties

Label 45738.2.a.io
Level $45738$
Weight $2$
Character orbit 45738.a
Self dual yes
Analytic conductor $365.220$
Dimension $12$

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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 = [12,-12,0,12,-10,0,12,-12,0,10,0,0,5,-12,0,12,3,0,4,-10,0,0,-5, 0,10,-5,0,12,0,0,16,-12,0,-3,-10,0,9,-4,0,10,-3,0,-4,0,0,5,-10,0,12,-10, 0,5,-16,0,0,-12,0,0,-13,0,3,-16,0,12,-14,0,-12,3,0,10,37,0,3,-9,0,4,0, 0,10,-10,0,3,-44,0,36,4,0,0,-33,0,5,-5,0,10,-49,0,8,-12,0,10] 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: \(12\)
Coefficient field: \(\mathbb{Q}[x]/(x^{12} - \cdots)\)
Copy content comment:defining polynomial
 
Copy content gp:f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{12} - 2 x^{11} - 29 x^{10} + 45 x^{9} + 310 x^{8} - 286 x^{7} - 1498 x^{6} + 189 x^{5} + 2960 x^{4} + \cdots - 1 \) 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.

\(\operatorname{Tr}(f)(q) = \) \( 12 q - 12 q^{2} + 12 q^{4} - 10 q^{5} + 12 q^{7} - 12 q^{8} + 10 q^{10} + 5 q^{13} - 12 q^{14} + 12 q^{16} + 3 q^{17} + 4 q^{19} - 10 q^{20} - 5 q^{23} + 10 q^{25} - 5 q^{26} + 12 q^{28} + 16 q^{31} - 12 q^{32}+ \cdots - 12 q^{98}+O(q^{100}) \) 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.