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Properties

Label 45486.2.a.q
Level $45486$
Weight $2$
Character orbit 45486.a
Self dual yes
Analytic conductor $363.208$
Dimension $1$

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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 = [1,-1,0,1,1,0,-1,-1,0,-1,0,0,-1,1,0,1,4,0,0,1,0,0,7,0,-4,1,0, -1,-8,0,10,-1,0,-4,-1,0,8,0,0,-1,0,0,-6,0,0,-7,8,0,1,4,0,-1,-10,0,0,1, 0,8,-5,0,-7,-10,0,1,-1,0,-14,4,0,1,7,0,4,-8,0,0,0,0,8,1,0,0,3,0,4,6,0, 0,-6,0,1,7,0,-8,0,0,-18,-1,0,-4] 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: \(1\)
Coefficient field: \(\mathbb{Q}\)
Coefficient ring: \(\mathbb{Z}\)
Coefficient ring index: \( 1 \)
Twist minimal: not computed
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

$q$-expansion

Copy content comment:q-expansion
 
Copy content sage:f.q_expansion() # note that sage often uses an isomorphic number field
 
Copy content gp:mfcoefs(f, 20)
 
\(f(q)\) \(=\) \( q - q^{2} + q^{4} + q^{5} - q^{7} - q^{8} - q^{10} - q^{13} + q^{14} + q^{16} + 4 q^{17} + q^{20} + 7 q^{23} - 4 q^{25} + q^{26} - q^{28} - 8 q^{29} + 10 q^{31} - q^{32} - 4 q^{34} - q^{35}+ \cdots - q^{98}+O(q^{100}) \) 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.