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Properties

Label 33462.2.a.db
Level $33462$
Weight $2$
Character orbit 33462.a
Self dual yes
Analytic conductor $267.195$
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] = [33462,2,Mod(1,33462)] 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("33462.1"); S:= CuspForms(chi, 2); N := Newforms(S);
 
Copy content sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(33462, base_ring=CyclotomicField(2)) chi = DirichletCharacter(H, H._module([0, 0, 0])) N = Newforms(chi, 2, names="a")
 
Level: \( N \) \(=\) \( 33462 = 2 \cdot 3^{2} \cdot 11 \cdot 13^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 33462.a (trivial)

Newform invariants

Copy content comment:select newform
 
Copy content sage:traces = [1,1,0,1,2,0,4,1,0,2,-1,0,0,4,0,1,-2,0,-4,2,0,-1,-4,0,-1,0,0, 4,-6,0,0,1,0,-2,8,0,-6,-4,0,2,-6,0,4,-1,0,-4,-12,0,9,-1,0,0,-2,0,-2,4, 0,-6,12,0,-14,0,0,1,0,0,-4,-2,0,8,-12,0,6,-6,0,-4,-4,0,-4,2,0,-6,4,0,-4, 4,0,-1,10,0,0,-4,0,-12,-8,0,14,9,0,-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: \(267.195415244\)
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)
 
\(f(q)\) \(=\) \( q + q^{2} + q^{4} + 2 q^{5} + 4 q^{7} + q^{8} + 2 q^{10} - q^{11} + 4 q^{14} + q^{16} - 2 q^{17} - 4 q^{19} + 2 q^{20} - q^{22} - 4 q^{23} - q^{25} + 4 q^{28} - 6 q^{29} + q^{32} - 2 q^{34} + 8 q^{35}+ \cdots + 9 q^{98}+O(q^{100}) \) Copy content Toggle raw display

Atkin-Lehner signs

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

Inner twists

Inner twists of this newform have not been computed.

Twists

Twists of this newform have not been computed.