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Properties

Label 32368.2.a.w
Level $32368$
Weight $2$
Character orbit 32368.a
Self dual yes
Analytic conductor $258.460$
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] = [32368,2,Mod(1,32368)] 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("32368.1"); S:= CuspForms(chi, 2); N := Newforms(S);
 
Copy content sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(32368, base_ring=CyclotomicField(2)) chi = DirichletCharacter(H, H._module([0, 0, 0, 0])) N = Newforms(chi, 2, names="a")
 
Level: \( N \) \(=\) \( 32368 = 2^{4} \cdot 7 \cdot 17^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 32368.a (trivial)

Newform invariants

Copy content comment:select newform
 
Copy content sage:traces = [1,0,1,0,-3,0,1,0,-2,0,0,0,5,0,-3,0,0,0,4,0,1,0,3,0,4,0,-5,0, -6,0,2,0,0,0,-3,0,4,0,5,0,-6,0,4,0,6,0,-6,0,1,0,0,0,-12,0,0,0,4,0,-12, 0,1,0,-2,0,-15,0,-8,0,3,0,-9,0,16,0,4,0,0,0,8,0,1,0,3,0,0,0,-6,0,6,0,5, 0,2,0,-12,0,10,0,0,0] 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: \(258.459781262\)
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)
 
\(f(q)\) \(=\) \( q + q^{3} - 3 q^{5} + q^{7} - 2 q^{9} + 5 q^{13} - 3 q^{15} + 4 q^{19} + q^{21} + 3 q^{23} + 4 q^{25} - 5 q^{27} - 6 q^{29} + 2 q^{31} - 3 q^{35} + 4 q^{37} + 5 q^{39} - 6 q^{41} + 4 q^{43} + 6 q^{45}+ \cdots + 10 q^{97}+O(q^{100}) \) Copy content Toggle raw display

Atkin-Lehner signs

\( p \) Sign
\(2\) \( -1 \)
\(7\) \( -1 \)
\(17\) \( +1 \)

Inner twists

Inner twists of this newform have not been computed.

Twists

Twists of this newform have not been computed.