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Properties

Label 30064.2.a.d
Level 3006430064
Weight 22
Character orbit 30064.a
Self dual yes
Analytic conductor 240.062240.062
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] = [30064,2,Mod(1,30064)] 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("30064.1"); S:= CuspForms(chi, 2); N := Newforms(S);
 
Copy content sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(30064, base_ring=CyclotomicField(2)) chi = DirichletCharacter(H, H._module([0, 0, 0])) N = Newforms(chi, 2, names="a")
 
Level: N N == 30064=24⋅1879 30064 = 2^{4} \cdot 1879
Weight: k k == 2 2
Character orbit: [χ][\chi] == 30064.a (trivial)

Newform invariants

Copy content comment:select newform
 
Copy content sage:traces = [1,0,0,0,-1,0,1,0,-3,0,2,0,4,0,0,0,1,0,0,0,0,0,-6,0,-4,0,0,0, -3,0,-2,0,0,0,-1,0,-8,0,0,0,-12,0,-1,0,3,0,-3,0,-6,0,0,0,5,0,-2,0,0,0, 12,0,2,0,-3,0,-4,0,7,0,0,0,-9,0,-3,0,0,0,2,0,14,0,9,0,15,0,-1,0,0,0,-15, 0,4,0,0,0,0,0,-10,0,-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: 240.062248637240.062248637
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+q7−3q9+2q11+4q13+q17−6q23−4q25−3q29−2q31−q35−8q37−12q41−q43+3q45−3q47−6q49+5q53−2q55+⋯−6q99+O(q100) q - q^{5} + q^{7} - 3 q^{9} + 2 q^{11} + 4 q^{13} + q^{17} - 6 q^{23} - 4 q^{25} - 3 q^{29} - 2 q^{31} - q^{35} - 8 q^{37} - 12 q^{41} - q^{43} + 3 q^{45} - 3 q^{47} - 6 q^{49} + 5 q^{53} - 2 q^{55}+ \cdots - 6 q^{99}+O(q^{100}) Copy content Toggle raw display

Atkin-Lehner signs

p p Sign
22 −1 -1
18791879 +1 +1

Inner twists

Inner twists of this newform have not been computed.

Twists

Twists of this newform have not been computed.