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Properties

Label 32340.2.a.d
Level $32340$
Weight $2$
Character orbit 32340.a
Self dual yes
Analytic conductor $258.236$
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] = [32340,2,Mod(1,32340)] 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("32340.1"); S:= CuspForms(chi, 2); N := Newforms(S);
 
Copy content sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(32340, base_ring=CyclotomicField(2)) chi = DirichletCharacter(H, H._module([0, 0, 0, 0, 0])) N = Newforms(chi, 2, names="a")
 
Level: \( N \) \(=\) \( 32340 = 2^{2} \cdot 3 \cdot 5 \cdot 7^{2} \cdot 11 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 32340.a (trivial)

Newform invariants

Copy content comment:select newform
 
Copy content sage:traces = [1,0,-1,0,-1,0,0,0,1,0,-1,0,7,0,1,0,2,0,0,0,0,0,2,0,1,0,-1,0, 2,0,-3,0,1,0,0,0,12,0,-7,0,6,0,1,0,-1,0,-10,0,0,0,-2,0,0,0,1,0,0,0,7,0, 0,0,0,0,-7,0,-4,0,-2,0,9,0,9,0,-1,0,0,0,-6,0,1,0,11,0,-2,0,-2,0,7,0,0, 0,3,0,0,0,-8,0,-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: \(258.236200137\)
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)
 
\(f(q)\) \(=\) \( q - q^{3} - q^{5} + q^{9} - q^{11} + 7 q^{13} + q^{15} + 2 q^{17} + 2 q^{23} + q^{25} - q^{27} + 2 q^{29} - 3 q^{31} + q^{33} + 12 q^{37} - 7 q^{39} + 6 q^{41} + q^{43} - q^{45} - 10 q^{47} - 2 q^{51}+ \cdots - q^{99}+O(q^{100}) \) Copy content Toggle raw display

Atkin-Lehner signs

\( p \) Sign
\(2\) \( -1 \)
\(3\) \( +1 \)
\(5\) \( +1 \)
\(7\) \( +1 \)
\(11\) \( +1 \)

Inner twists

Inner twists of this newform have not been computed.

Twists

Twists of this newform have not been computed.