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Properties

Label 33120.2.a.o
Level 3312033120
Weight 22
Character orbit 33120.a
Self dual yes
Analytic conductor 264.465264.465
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] = [33120,2,Mod(1,33120)] 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("33120.1"); S:= CuspForms(chi, 2); N := Newforms(S);
 
Copy content sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(33120, base_ring=CyclotomicField(2)) chi = DirichletCharacter(H, H._module([0, 0, 0, 0, 0])) N = Newforms(chi, 2, names="a")
 
Level: N N == 33120=25⋅32⋅5⋅23 33120 = 2^{5} \cdot 3^{2} \cdot 5 \cdot 23
Weight: k k == 2 2
Character orbit: [χ][\chi] == 33120.a (trivial)

Newform invariants

Copy content comment:select newform
 
Copy content sage:traces = [1,0,0,0,-1,0,2,0,0,0,6,0,2,0,0,0,4,0,-8,0,0,0,-1,0,1,0,0,0,-6, 0,-4,0,0,0,-2,0,12,0,0,0,-2,0,-4,0,0,0,0,0,-3,0,0,0,6,0,-6,0,0,0,0,0,-4, 0,0,0,-2,0,-4,0,0,0,-8,0,6,0,0,0,12,0,2,0,0,0,6,0,-4,0,0,0,0,0,4,0,0,0, 8,0,-14,0,0,0] 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: 264.464531494264.464531494
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−q5+2q7+6q11+2q13+4q17−8q19−q23+q25−6q29−4q31−2q35+12q37−2q41−4q43−3q49+6q53−6q55−4q61−2q65+⋯−14q97+O(q100) q - q^{5} + 2 q^{7} + 6 q^{11} + 2 q^{13} + 4 q^{17} - 8 q^{19} - q^{23} + q^{25} - 6 q^{29} - 4 q^{31} - 2 q^{35} + 12 q^{37} - 2 q^{41} - 4 q^{43} - 3 q^{49} + 6 q^{53} - 6 q^{55} - 4 q^{61} - 2 q^{65}+ \cdots - 14 q^{97}+O(q^{100}) Copy content Toggle raw display

Atkin-Lehner signs

p p Sign
22 +1 +1
33 −1 -1
55 +1 +1
2323 +1 +1

Inner twists

Inner twists of this newform have not been computed.

Twists

Twists of this newform have not been computed.