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Properties

Label 16245.2.a.q
Level 1624516245
Weight 22
Character orbit 16245.a
Self dual yes
Analytic conductor 129.717129.717
Dimension 22

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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] = [16245,2,Mod(1,16245)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)
 
Copy content sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(16245, base_ring=CyclotomicField(2)) chi = DirichletCharacter(H, H._module([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("16245.1"); S:= CuspForms(chi, 2); N := Newforms(S);
 
Level: N N == 16245=32⋅5⋅192 16245 = 3^{2} \cdot 5 \cdot 19^{2}
Weight: k k == 2 2
Character orbit: [χ][\chi] == 16245.a (trivial)

Newform invariants

Copy content comment:select newform
 
Copy content sage:traces = [2,-2,0,2,2,0,-2,-6,0,-2,0,0,2,10,0,6,8,0,0,2,0,8,-4,0,2,-10, 0,-18,-8,0,-10,6,0,-16,-2,0,-10,0,0,-6,0,0,10,-16,0,12,12,0,4,-2,0,18, 4,0,0,14,0,-8,0,0,6,10,0,-14,2,0,-6,24,0,10,-20,0,2,18,0,0,16,0,-18,6, 0,-8,16,0,8,-2,0,8,-8,0,-18,-20,0,-20,0,0,-12,-20,0,2] 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: 129.716978084129.716978084
Dimension: 22
Coefficient field: Q(2)\Q(\sqrt{2})
Copy content comment:defining polynomial
 
Copy content gp:f.mod \\ as an extension of the character field
 
Defining polynomial: x2−2 x^{2} - 2 Copy content Toggle raw display
Twist minimal: not computed
Fricke sign: +1+1
Sato-Tate group: SU(2)\mathrm{SU}(2)

qq-expansion

The algebraic qq-expansion of this newform has not been computed, but we have computed the trace expansion.

Tr⁡(f)(q)=\operatorname{Tr}(f)(q) = 2q−2q2+2q4+2q5−2q7−6q8−2q10+2q13+10q14+6q16+8q17+2q20+8q22−4q23+2q25−10q26−18q28−8q29−10q31+6q32+⋯−20q98+O(q100) 2 q - 2 q^{2} + 2 q^{4} + 2 q^{5} - 2 q^{7} - 6 q^{8} - 2 q^{10} + 2 q^{13} + 10 q^{14} + 6 q^{16} + 8 q^{17} + 2 q^{20} + 8 q^{22} - 4 q^{23} + 2 q^{25} - 10 q^{26} - 18 q^{28} - 8 q^{29} - 10 q^{31} + 6 q^{32}+ \cdots - 20 q^{98}+O(q^{100}) Copy content Toggle raw display

Atkin-Lehner signs

p p Sign
33 −1 -1
55 −1 -1
1919 +1 +1

Inner twists

Inner twists of this newform have not been computed.

Twists

Twists of this newform have not been computed.