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Properties

Label 21450.2.a.bs
Level $21450$
Weight $2$
Character orbit 21450.a
Self dual yes
Analytic conductor $171.279$
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] = [21450,2,Mod(1,21450)] 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("21450.1"); S:= CuspForms(chi, 2); N := Newforms(S);
 
Copy content sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(21450, base_ring=CyclotomicField(2)) chi = DirichletCharacter(H, H._module([0, 0, 0, 0])) N = Newforms(chi, 2, names="a")
 
Level: \( N \) \(=\) \( 21450 = 2 \cdot 3 \cdot 5^{2} \cdot 11 \cdot 13 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 21450.a (trivial)

Newform invariants

Copy content comment:select newform
 
Copy content sage:traces = [1,1,-1,1,0,-1,-2,1,1,0,1,-1,1,-2,0,1,-6,1,-3,0,2,1,2,-1,0,1, -1,-2,1,0,2,1,-1,-6,0,1,-1,-3,-1,0,3,2,4,1,0,2,7,-1,-3,0,6,1,13,-1,0,-2, 3,1,0,0,-10,2,-2,1,0,-1,-5,-6,-2,0,-9,1,8,-1,0,-3,-2,-1,-11,0,1,3,10,2, 0,4,-1,1,-14,0,-2,2,-2,7,0,-1,12,-3,1,0] 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: \(171.279112336\)
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)
 
\(f(q)\) \(=\) \( q + q^{2} - q^{3} + q^{4} - q^{6} - 2 q^{7} + q^{8} + q^{9} + q^{11} - q^{12} + q^{13} - 2 q^{14} + q^{16} - 6 q^{17} + q^{18} - 3 q^{19} + 2 q^{21} + q^{22} + 2 q^{23} - q^{24} + q^{26}+ \cdots + q^{99}+O(q^{100}) \) Copy content Toggle raw display

Atkin-Lehner signs

\( p \) Sign
\(2\) \( -1 \)
\(3\) \( +1 \)
\(5\) \( -1 \)
\(11\) \( -1 \)
\(13\) \( -1 \)

Inner twists

Inner twists of this newform have not been computed.

Twists

Twists of this newform have not been computed.