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Properties

Label 45662.2.a.i
Level $45662$
Weight $2$
Character orbit 45662.a
Self dual yes
Analytic conductor $364.613$
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] = [45662,2,Mod(1,45662)] 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("45662.1"); S:= CuspForms(chi, 2); N := Newforms(S);
 
Copy content sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(45662, base_ring=CyclotomicField(2)) chi = DirichletCharacter(H, H._module([0, 0])) N = Newforms(chi, 2, names="a")
 
Level: \( N \) \(=\) \( 45662 = 2 \cdot 17^{2} \cdot 79 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 45662.a (trivial)

Newform invariants

Copy content comment:select newform
 
Copy content sage:traces = [1,-1,1,1,1,-1,3,-1,-2,-1,-4,1,-7,-3,1,1,0,2,-6,1,3,4,-6,-1,-4, 7,-5,3,-4,-1,-8,-1,-4,0,3,-2,-10,6,-7,-1,8,-3,-8,-4,-2,6,-3,1,2,4,0,-7, 2,5,-4,-3,-6,4,1,1,0,8,-6,1,-7,4,-4,0,-6,-3,11,2,6,10,-4,-6,-12,7,1,1, 1,-8,6,3,0,8,-4,4,-15,2,-21,-6,-8,3,-6,-1,-1,-2,8,-4] 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: \(364.612905710\)
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)
 
\(f(q)\) \(=\) \( q - q^{2} + q^{3} + q^{4} + q^{5} - q^{6} + 3 q^{7} - q^{8} - 2 q^{9} - q^{10} - 4 q^{11} + q^{12} - 7 q^{13} - 3 q^{14} + q^{15} + q^{16} + 2 q^{18} - 6 q^{19} + q^{20} + 3 q^{21} + 4 q^{22}+ \cdots + 8 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Atkin-Lehner signs

\( p \) Sign
\(2\) \( +1 \)
\(17\) \( +1 \)
\(79\) \( -1 \)

Inner twists

Inner twists of this newform have not been computed.

Twists

Twists of this newform have not been computed.