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Properties

Label 45968.2.a.i
Level $45968$
Weight $2$
Character orbit 45968.a
Self dual yes
Analytic conductor $367.056$
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] = [45968,2,Mod(1,45968)] 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("45968.1"); S:= CuspForms(chi, 2); N := Newforms(S);
 
Copy content sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(45968, base_ring=CyclotomicField(2)) chi = DirichletCharacter(H, H._module([0, 0, 0, 0])) N = Newforms(chi, 2, names="a")
 
Level: \( N \) \(=\) \( 45968 = 2^{4} \cdot 13^{2} \cdot 17 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 45968.a (trivial)

Newform invariants

Copy content comment:select newform
 
Copy content sage:traces = [1,0,0,0,-2,0,4,0,-3,0,-2,0,0,0,0,0,-1,0,0,0,0,0,-2,0,-1,0,0, 0,8,0,-8,0,0,0,-8,0,6,0,0,0,-12,0,-4,0,6,0,-8,0,9,0,0,0,-6,0,4,0,0,0,-4, 0,-8,0,-12,0,0,0,-8,0,0,0,-8,0,-8,0,0,0,-8,0,10,0,9,0,0,0,2,0,0,0,-6,0, 0,0,0,0,0,0,16,0,6,0] 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: \(367.056328011\)
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)
 
\(f(q)\) \(=\) \( q - 2 q^{5} + 4 q^{7} - 3 q^{9} - 2 q^{11} - q^{17} - 2 q^{23} - q^{25} + 8 q^{29} - 8 q^{31} - 8 q^{35} + 6 q^{37} - 12 q^{41} - 4 q^{43} + 6 q^{45} - 8 q^{47} + 9 q^{49} - 6 q^{53} + 4 q^{55} - 4 q^{59}+ \cdots + 6 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Atkin-Lehner signs

\( p \) Sign
\(2\) \( -1 \)
\(13\) \( +1 \)
\(17\) \( +1 \)

Inner twists

Inner twists of this newform have not been computed.

Twists

Twists of this newform have not been computed.