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Properties

Label 45738.2.a.id
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,-10,0,10,4,0,10,-10,0,-4,0,0,-2,-10,0,10,0,0,-4,4,0,0,14, 0,12,2,0,10,0,0,4,-10,0,0,4,0,0,4,0,-4,10,0,2,0,0,-14,30,0,10,-12,0,-2, 14,0,0,-10,0,0,26,0,-6,-4,0,10,24,0,-14,0,0,-4,14,0,-40,0,0,-4,0,0,-20, 4,0,-10,26,0,-16,-2,0,0,44,0,-2,14,0,-30,12,0,-16,-10,0,12] 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: \( x^{10} - 4x^{9} - 23x^{8} + 94x^{7} + 167x^{6} - 650x^{5} - 620x^{4} + 1574x^{3} + 1174x^{2} - 558x + 33 \) 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.

\(\operatorname{Tr}(f)(q) = \) \( 10 q - 10 q^{2} + 10 q^{4} + 4 q^{5} + 10 q^{7} - 10 q^{8} - 4 q^{10} - 2 q^{13} - 10 q^{14} + 10 q^{16} - 4 q^{19} + 4 q^{20} + 14 q^{23} + 12 q^{25} + 2 q^{26} + 10 q^{28} + 4 q^{31} - 10 q^{32} + 4 q^{35}+ \cdots - 10 q^{98}+O(q^{100}) \) 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.