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Properties

Label 45486.2.a.dk
Level $45486$
Weight $2$
Character orbit 45486.a
Self dual yes
Analytic conductor $363.208$
Dimension $2$

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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] = [45486,2,Mod(1,45486)] 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("45486.1"); S:= CuspForms(chi, 2); N := Newforms(S);
 
Copy content sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(45486, base_ring=CyclotomicField(2)) chi = DirichletCharacter(H, H._module([0, 0, 0])) N = Newforms(chi, 2, names="a")
 
Level: \( N \) \(=\) \( 45486 = 2 \cdot 3^{2} \cdot 7 \cdot 19^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 45486.a (trivial)

Newform invariants

Copy content comment:select newform
 
Copy content sage:traces = [2,2,0,2,4,0,-2,2,0,4,2,0,-4,-2,0,2,2,0,0,4,0,2,-12,0,-2,-4,0, -2,0,0,-2,2,0,2,-4,0,2,0,0,4,4,0,-4,2,0,-12,2,0,2,-2,0,-4,-8,0,4,-2,0, 0,-12,0,-4,-2,0,2,-8,0,2,2,0,-4,16,0,8,2,0,0,-2,0,16,4,0,4,16,0,4,-4,0, 2,16,0,4,-12,0,2,0,0,18,2,0,-2] 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: \(363.207538634\)
Dimension: \(2\)
Coefficient field: \(\Q(\sqrt{17}) \)
Copy content comment:defining polynomial
 
Copy content gp:f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{2} - x - 4 \) 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.

\(\operatorname{Tr}(f)(q) = \) \( 2 q + 2 q^{2} + 2 q^{4} + 4 q^{5} - 2 q^{7} + 2 q^{8} + 4 q^{10} + 2 q^{11} - 4 q^{13} - 2 q^{14} + 2 q^{16} + 2 q^{17} + 4 q^{20} + 2 q^{22} - 12 q^{23} - 2 q^{25} - 4 q^{26} - 2 q^{28} - 2 q^{31} + 2 q^{32}+ \cdots + 2 q^{98}+O(q^{100}) \) Copy content Toggle raw display

Atkin-Lehner signs

\( p \) Sign
\(2\) \( -1 \)
\(3\) \( +1 \)
\(7\) \( +1 \)
\(19\) \( +1 \)

Inner twists

Inner twists of this newform have not been computed.

Twists

Twists of this newform have not been computed.