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Properties

Label 18150.2.a.cj
Level $18150$
Weight $2$
Character orbit 18150.a
Self dual yes
Analytic conductor $144.928$
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] = [18150,2,Mod(1,18150)] 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("18150.1"); S:= CuspForms(chi, 2); N := Newforms(S);
 
Copy content sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(18150, base_ring=CyclotomicField(2)) chi = DirichletCharacter(H, H._module([0, 0, 0])) N = Newforms(chi, 2, names="a")
 
Level: \( N \) \(=\) \( 18150 = 2 \cdot 3 \cdot 5^{2} \cdot 11^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 18150.a (trivial)

Newform invariants

Copy content comment:select newform
 
Copy content sage:traces = [1,1,-1,1,0,-1,3,1,1,0,0,-1,4,3,0,1,-7,1,-5,0,-3,0,1,-1,0,4,-1, 3,10,0,2,1,0,-7,0,1,7,-5,-4,0,3,-3,4,0,0,1,-13,-1,2,0,7,4,-4,-1,0,3,5, 10,-5,0,-12,2,3,1,0,0,12,-7,-1,0,-3,1,4,7,0,-5,0,-4,15,0,1,3,14,-3,0,4, -10,0,0,0,12,1,-2,-13,0,-1,7,2,0,0] 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: \(144.928479669\)
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)
 
\(f(q)\) \(=\) \( q + q^{2} - q^{3} + q^{4} - q^{6} + 3 q^{7} + q^{8} + q^{9} - q^{12} + 4 q^{13} + 3 q^{14} + q^{16} - 7 q^{17} + q^{18} - 5 q^{19} - 3 q^{21} + q^{23} - q^{24} + 4 q^{26} - q^{27} + 3 q^{28}+ \cdots + 2 q^{98}+O(q^{100}) \) Copy content Toggle raw display

Atkin-Lehner signs

\( p \) Sign
\(2\) \( -1 \)
\(3\) \( +1 \)
\(5\) \( -1 \)
\(11\) \( -1 \)

Inner twists

Inner twists of this newform have not been computed.

Twists

Twists of this newform have not been computed.