Properties

Label 32400.2.a.g
Level 3240032400
Weight 22
Character orbit 32400.a
Self dual yes
Analytic conductor 258.715258.715
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] = [32400,2,Mod(1,32400)] 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("32400.1"); S:= CuspForms(chi, 2); N := Newforms(S);
 
Copy content sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(32400, base_ring=CyclotomicField(2)) chi = DirichletCharacter(H, H._module([0, 0, 0, 0])) N = Newforms(chi, 2, names="a")
 
Level: N N == 32400=243452 32400 = 2^{4} \cdot 3^{4} \cdot 5^{2}
Weight: k k == 2 2
Character orbit: [χ][\chi] == 32400.a (trivial)

Newform invariants

Copy content comment:select newform
 
Copy content sage:traces = [1,0,0,0,0,0,-4,0,0,0,0,0,1,0,0,0,3,0,4,0,0,0,0,0,0,0,0,0,9,0, 4,0,0,0,0,0,1,0,0,0,6,0,8,0,0,0,-12,0,9,0,0,0,6,0,0,0,0,0,0,0,-1,0,0,0, 0,0,-4,0,0,0,12,0,-11,0,0,0,0,0,16,0,0,0,-12,0,0,0,0,0,-3,0,-4,0,0,0,0, 0,-2,0,0,0] 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: 258.715302549258.715302549
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) == q4q7+q13+3q17+4q19+9q29+4q31+q37+6q41+8q4312q47+9q49+6q53q614q67+12q7111q73+16q7912q83+2q97+O(q100) q - 4 q^{7} + q^{13} + 3 q^{17} + 4 q^{19} + 9 q^{29} + 4 q^{31} + q^{37} + 6 q^{41} + 8 q^{43} - 12 q^{47} + 9 q^{49} + 6 q^{53} - q^{61} - 4 q^{67} + 12 q^{71} - 11 q^{73} + 16 q^{79} - 12 q^{83}+ \cdots - 2 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

Inner twists

Inner twists of this newform have not been computed.

Twists

Twists of this newform have not been computed.