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Properties

Label 43350.2.a.dd
Level $43350$
Weight $2$
Character orbit 43350.a
Self dual yes
Analytic conductor $346.151$
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] = [43350,2,Mod(1,43350)] 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("43350.1"); S:= CuspForms(chi, 2); N := Newforms(S);
 
Copy content sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(43350, base_ring=CyclotomicField(2)) chi = DirichletCharacter(H, H._module([0, 0, 0])) N = Newforms(chi, 2, names="a")
 
Level: \( N \) \(=\) \( 43350 = 2 \cdot 3 \cdot 5^{2} \cdot 17^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 43350.a (trivial)

Newform invariants

Copy content comment:select newform
 
Copy content sage:traces = [1,1,1,1,0,1,-1,1,1,0,-3,1,4,-1,0,1,0,1,-1,0,-1,-3,0,1,0,4,1, -1,0,0,-5,1,-3,0,0,1,11,-1,4,0,-6,-1,-5,-3,0,0,3,1,-6,0,0,4,9,1,0,-1,-1, 0,0,0,-14,-5,-1,1,0,-3,1,0,0,0,-6,1,2,11,0,-1,3,4,-17,0,1,-6,0,-1,0,-5, 0,-3,-6,0,-4,0,-5,3,0,1,2,-6,-3,0] 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: \(346.151492762\)
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)
 
\(f(q)\) \(=\) \( q + q^{2} + q^{3} + q^{4} + q^{6} - q^{7} + q^{8} + q^{9} - 3 q^{11} + q^{12} + 4 q^{13} - q^{14} + q^{16} + q^{18} - q^{19} - q^{21} - 3 q^{22} + q^{24} + 4 q^{26} + q^{27} - q^{28} - 5 q^{31}+ \cdots - 3 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Atkin-Lehner signs

\( p \) Sign
\(2\) \( -1 \)
\(3\) \( -1 \)
\(5\) \( +1 \)
\(17\) \( +1 \)

Inner twists

Inner twists of this newform have not been computed.

Twists

Twists of this newform have not been computed.