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Properties

Label 46410.2.a.p
Level 4641046410
Weight 22
Character orbit 46410.a
Self dual yes
Analytic conductor 370.586370.586
Dimension 11
CM no
Inner twists 11

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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] = [46410,2,Mod(1,46410)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)
 
Copy content sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(46410, base_ring=CyclotomicField(2)) chi = DirichletCharacter(H, H._module([0, 0, 0, 0, 0])) N = Newforms(chi, 2, names="a")
 
Copy content magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("46410.1"); S:= CuspForms(chi, 2); N := Newforms(S);
 
Level: N N == 46410=2⋅3⋅5⋅7⋅13⋅17 46410 = 2 \cdot 3 \cdot 5 \cdot 7 \cdot 13 \cdot 17
Weight: k k == 2 2
Character orbit: [χ][\chi] == 46410.a (trivial)

Newform invariants

Copy content comment:select newform
 
Copy content sage:traces = [1,-1,-1,1,1,1,1,-1,1,-1,0,-1,-1,-1,-1,1,-1,-1,4,1,-1,0,-4,1, 1,1,-1,1,-2,1,-8,-1,0,1,1,1,-6,-4,1,-1,2,1,8,0,1,4,-4,-1,1,-1,1,-1,6,1, 0,-1,-4,2,-4,-1,-6,8,1,1,-1,0,-4,-1,4,-1,-8,-1,-14,6,-1,4,0,-1,16,1,1, -2,12,-1,-1,-8,2,0,2,-1,-1,-4,8,4,4,1,2,-1,0,1] 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: 370.585715781370.585715781
Dimension: 11
Coefficient field: Q\mathbb{Q}
Coefficient ring: Z\mathbb{Z}
Coefficient ring index: 1 1
Twist minimal: yes
Fricke sign: +1+1
Sato-Tate group: SU(2)\mathrm{SU}(2)

qq-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)f(q) == q−q2−q3+q4+q5+q6+q7−q8+q9−q10−q12−q13−q14−q15+q16−q17−q18+4q19+q20−q21−4q23+q24+⋯−q98+O(q100) q - q^{2} - q^{3} + q^{4} + q^{5} + q^{6} + q^{7} - q^{8} + q^{9} - q^{10} - q^{12} - q^{13} - q^{14} - q^{15} + q^{16} - q^{17} - q^{18} + 4 q^{19} + q^{20} - q^{21} - 4 q^{23} + q^{24}+ \cdots - q^{98}+O(q^{100}) Copy content Toggle raw display

Atkin-Lehner signs

p p Sign
22 +1 +1
33 +1 +1
55 −1 -1
77 −1 -1
1313 +1 +1
1717 +1 +1

Inner twists

This newform does not admit any (nontrivial) inner twists.

Twists

Twists of this newform have not been computed.