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Properties

Label 35154.2.a.br
Level 3515435154
Weight 22
Character orbit 35154.a
Self dual yes
Analytic conductor 280.706280.706
Dimension 1515

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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] = [35154,2,Mod(1,35154)] 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("35154.1"); S:= CuspForms(chi, 2); N := Newforms(S);
 
Copy content sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(35154, base_ring=CyclotomicField(2)) chi = DirichletCharacter(H, H._module([0, 0, 0])) N = Newforms(chi, 2, names="a")
 
Level: N N == 35154=2⋅34⋅7⋅31 35154 = 2 \cdot 3^{4} \cdot 7 \cdot 31
Weight: k k == 2 2
Character orbit: [χ][\chi] == 35154.a (trivial)

Newform invariants

Copy content comment:select newform
 
Copy content sage:traces = [15,15,0,15,-2,0,15,15,0,-2,1,0,-14,15,0,15,-2,0,9,-2,0,1,-7, 0,-15,-14,0,15,-17,0,-15,15,0,-2,-2,0,-7,9,0,-2,-6,0,-21,1,0,-7,-4,0,15, -15,0,-14,-13,0,-45,15,0,-17,-22,0,-35,-15,0,15,-35,0,2,-2,0,-2,-22,0, -8,-7,0,9,1,0,-70,-2,0,-6,-5,0,-49,-21,0,1,-19,0,-14,-7,0,-4,31,0,-6,15, 0,-15] 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: 280.706103266280.706103266
Dimension: 1515
Coefficient field: Q[x]/(x15−⋯ )\mathbb{Q}[x]/(x^{15} - \cdots)
Copy content comment:defining polynomial
 
Copy content gp:f.mod \\ as an extension of the character field
 
Defining polynomial: x15−2x14−28x13+59x12+265x11−571x10−1001x9+2093x8+1541x7+⋯−1 x^{15} - 2 x^{14} - 28 x^{13} + 59 x^{12} + 265 x^{11} - 571 x^{10} - 1001 x^{9} + 2093 x^{8} + 1541 x^{7} + \cdots - 1 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) = 15q+15q2+15q4−2q5+15q7+15q8−2q10+q11−14q13+15q14+15q16−2q17+9q19−2q20+q22−7q23−15q25−14q26+15q28+⋯+15q98+O(q100) 15 q + 15 q^{2} + 15 q^{4} - 2 q^{5} + 15 q^{7} + 15 q^{8} - 2 q^{10} + q^{11} - 14 q^{13} + 15 q^{14} + 15 q^{16} - 2 q^{17} + 9 q^{19} - 2 q^{20} + q^{22} - 7 q^{23} - 15 q^{25} - 14 q^{26} + 15 q^{28}+ \cdots + 15 q^{98}+O(q^{100}) Copy content Toggle raw display

Atkin-Lehner signs

p p Sign
22 −1 -1
33 +1 +1
77 −1 -1
3131 +1 +1

Inner twists

Inner twists of this newform have not been computed.

Twists

Twists of this newform have not been computed.