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Properties

Label 14450.2.a.o
Level 1445014450
Weight 22
Character orbit 14450.a
Self dual yes
Analytic conductor 115.384115.384
Dimension 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] = [14450,2,Mod(1,14450)] 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("14450.1"); S:= CuspForms(chi, 2); N := Newforms(S);
 
Copy content sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(14450, base_ring=CyclotomicField(2)) chi = DirichletCharacter(H, H._module([0, 0])) N = Newforms(chi, 2, names="a")
 
Level: N N == 14450=2⋅52⋅172 14450 = 2 \cdot 5^{2} \cdot 17^{2}
Weight: k k == 2 2
Character orbit: [χ][\chi] == 14450.a (trivial)

Newform invariants

Copy content comment:select newform
 
Copy content sage:traces = [1,-1,2,1,0,-2,-3,-1,1,0,-3,2,-3,3,0,1,0,-1,-4,0,-6,3,5,-2,0, 3,-4,-3,8,0,-8,-1,-6,0,0,1,-2,4,-6,0,-6,6,-10,-3,0,-5,3,2,2,0,0,-3,3,4, 0,3,-8,-8,11,0,-12,8,-3,1,0,6,-8,0,10,0,12,-1,2,2,0,-4,9,6,-14,0,-11,6, 16,-6,0,10,16,3,5,0,9,5,-16,-3,0,-2,18,-2,-3,0] 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: 115.383830921115.383830921
Dimension: 11
Coefficient field: Q\mathbb{Q}
Coefficient ring: Z\mathbb{Z}
Coefficient ring index: 1 1
Twist minimal: not computed
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+2q3+q4−2q6−3q7−q8+q9−3q11+2q12−3q13+3q14+q16−q18−4q19−6q21+3q22+5q23−2q24+3q26−4q27+⋯−3q99+O(q100) q - q^{2} + 2 q^{3} + q^{4} - 2 q^{6} - 3 q^{7} - q^{8} + q^{9} - 3 q^{11} + 2 q^{12} - 3 q^{13} + 3 q^{14} + q^{16} - q^{18} - 4 q^{19} - 6 q^{21} + 3 q^{22} + 5 q^{23} - 2 q^{24} + 3 q^{26} - 4 q^{27}+ \cdots - 3 q^{99}+O(q^{100}) Copy content Toggle raw display

Atkin-Lehner signs

p p Sign
22 +1 +1
55 −1 -1
1717 +1 +1

Inner twists

Inner twists of this newform have not been computed.

Twists

Twists of this newform have not been computed.