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Properties

Label 15680.2.a.bl
Level 1568015680
Weight 22
Character orbit 15680.a
Self dual yes
Analytic conductor 125.205125.205
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] = [15680,2,Mod(1,15680)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)
 
Copy content sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(15680, base_ring=CyclotomicField(2)) chi = DirichletCharacter(H, H._module([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("15680.1"); S:= CuspForms(chi, 2); N := Newforms(S);
 
Level: N N == 15680=26⋅5⋅72 15680 = 2^{6} \cdot 5 \cdot 7^{2}
Weight: k k == 2 2
Character orbit: [χ][\chi] == 15680.a (trivial)

Newform invariants

Copy content comment:select newform
 
Copy content sage:traces = [1,0,-1,0,1,0,0,0,-2,0,-3,0,-7,0,-1,0,5,0,-4,0,0,0,4,0,1,0,5, 0,5,0,-2,0,3,0,0,0,0,0,7,0,-6,0,8,0,-2,0,9,0,0,0,-5,0,0,0,-3,0,4,0,-12, 0,-6,0,0,0,-7,0,16,0,-4,0,4,0,14,0,-1,0,0,0,9,0,1,0,8,0,5,0,-5,0,6,0,0, 0,2,0,-4,0,-3,0,6,0] 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: 125.205430369125.205430369
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−q3+q5−2q9−3q11−7q13−q15+5q17−4q19+4q23+q25+5q27+5q29−2q31+3q33+7q39−6q41+8q43−2q45+9q47+⋯+6q99+O(q100) q - q^{3} + q^{5} - 2 q^{9} - 3 q^{11} - 7 q^{13} - q^{15} + 5 q^{17} - 4 q^{19} + 4 q^{23} + q^{25} + 5 q^{27} + 5 q^{29} - 2 q^{31} + 3 q^{33} + 7 q^{39} - 6 q^{41} + 8 q^{43} - 2 q^{45} + 9 q^{47}+ \cdots + 6 q^{99}+O(q^{100}) Copy content Toggle raw display

Atkin-Lehner signs

p p Sign
22 +1 +1
55 −1 -1
77 −1 -1

Inner twists

Inner twists of this newform have not been computed.

Twists

Twists of this newform have not been computed.