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Properties

Label 33282.2.a.bf
Level $33282$
Weight $2$
Character orbit 33282.a
Self dual yes
Analytic conductor $265.758$
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] = [33282,2,Mod(1,33282)] 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("33282.1"); S:= CuspForms(chi, 2); N := Newforms(S);
 
Copy content sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(33282, base_ring=CyclotomicField(2)) chi = DirichletCharacter(H, H._module([0, 0])) N = Newforms(chi, 2, names="a")
 
Level: \( N \) \(=\) \( 33282 = 2 \cdot 3^{2} \cdot 43^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 33282.a (trivial)

Newform invariants

Copy content comment:select newform
 
Copy content sage:traces = [1,1,0,1,2,0,4,1,0,2,5,0,-6,4,0,1,-3,0,-7,2,0,5,-2,0,-1,-6,0, 4,-6,0,-2,1,0,-3,8,0,-4,-7,0,2,-11,0,0,5,0,-2,-10,0,9,-1,0,-6,-6,0,10, 4,0,-6,-3,0,4,-2,0,1,-12,0,15,-3,0,8,2,0,-9,-4,0,-7,20,0,14,2,0,-11,0, 0,-6,0,0,5,-1,0,-24,-2,0,-10,-14,0,5,9,0,-1] 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: \(265.758108007\)
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)
 
\(f(q)\) \(=\) \( q + q^{2} + q^{4} + 2 q^{5} + 4 q^{7} + q^{8} + 2 q^{10} + 5 q^{11} - 6 q^{13} + 4 q^{14} + q^{16} - 3 q^{17} - 7 q^{19} + 2 q^{20} + 5 q^{22} - 2 q^{23} - q^{25} - 6 q^{26} + 4 q^{28} - 6 q^{29}+ \cdots + 9 q^{98}+O(q^{100}) \) Copy content Toggle raw display

Atkin-Lehner signs

\( p \) Sign
\(2\) \( -1 \)
\(3\) \( -1 \)
\(43\) \( +1 \)

Inner twists

Inner twists of this newform have not been computed.

Twists

Twists of this newform have not been computed.