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Properties

Label 13650.2.a.ca
Level $13650$
Weight $2$
Character orbit 13650.a
Self dual yes
Analytic conductor $108.996$
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] = [13650,2,Mod(1,13650)] 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("13650.1"); S:= CuspForms(chi, 2); N := Newforms(S);
 
Copy content sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(13650, base_ring=CyclotomicField(2)) chi = DirichletCharacter(H, H._module([0, 0, 0, 0])) N = Newforms(chi, 2, names="a")
 
Level: \( N \) \(=\) \( 13650 = 2 \cdot 3 \cdot 5^{2} \cdot 7 \cdot 13 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 13650.a (trivial)

Newform invariants

Copy content comment:select newform
 
Copy content sage:traces = [1,1,-1,1,0,-1,1,1,1,0,-4,-1,1,1,0,1,2,1,8,0,-1,-4,4,-1,0,1,-1, 1,-2,0,4,1,4,2,0,1,-2,8,-1,0,6,-1,8,-4,0,4,-8,-1,1,0,-2,1,-6,-1,0,1,-8, -2,0,0,6,4,1,1,0,4,-4,2,-4,0,8,1,-6,-2,0,8,-4,-1,-8,0,1,6,-12,-1,0,8,2, -4,-2,0,1,4,-4,-8,0,-1,2,1,-4,0] 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: \(108.995798759\)
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)
 
\(f(q)\) \(=\) \( q + q^{2} - q^{3} + q^{4} - q^{6} + q^{7} + q^{8} + q^{9} - 4 q^{11} - q^{12} + q^{13} + q^{14} + q^{16} + 2 q^{17} + q^{18} + 8 q^{19} - q^{21} - 4 q^{22} + 4 q^{23} - q^{24} + q^{26} - q^{27}+ \cdots - 4 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Atkin-Lehner signs

\( p \) Sign
\(2\) \( -1 \)
\(3\) \( +1 \)
\(5\) \( +1 \)
\(7\) \( -1 \)
\(13\) \( -1 \)

Inner twists

Inner twists of this newform have not been computed.

Twists

Twists of this newform have not been computed.