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Properties

Label 42978.2.a.r
Level 4297842978
Weight 22
Character orbit 42978.a
Self dual yes
Analytic conductor 343.181343.181
Dimension 11
CM no
Inner twists 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] = [42978,2,Mod(1,42978)] 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("42978.1"); S:= CuspForms(chi, 2); N := Newforms(S);
 
Copy content sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(42978, base_ring=CyclotomicField(2)) chi = DirichletCharacter(H, H._module([0, 0, 0, 0])) N = Newforms(chi, 2, names="a")
 
Level: N N == 42978=2⋅3⋅13⋅19⋅29 42978 = 2 \cdot 3 \cdot 13 \cdot 19 \cdot 29
Weight: k k == 2 2
Character orbit: [χ][\chi] == 42978.a (trivial)

Newform invariants

Copy content comment:select newform
 
Copy content sage:traces = [1,1,1,1,-4,1,-2,1,1,-4,-3,1,1,-2,-4,1,-7,1,-1,-4,-2,-3,-6,1, 11,1,1,-2,-1,-4,-3,1,-3,-7,8,1,-2,-1,1,-4,-8,-2,-1,-3,-4,-6,-12,1,-3,11, -7,1,-11,1,12,-2,-1,-1,10,-4,7,-3,-2,1,-4,-3,-7,-7,-6,8,-3,1,-1,-2,11, -1,6,1,-10,-4,1,-8,-6,-2,28,-1,-1,-3,0,-4,-2,-6,-3,-12,4,1,-2,-3,-3,11] 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: 343.181057807343.181057807
Dimension: 11
Coefficient field: Q\mathbb{Q}
Coefficient ring: Z\mathbb{Z}
Coefficient ring index: 1 1
Twist minimal: yes
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+q2+q3+q4−4q5+q6−2q7+q8+q9−4q10−3q11+q12+q13−2q14−4q15+q16−7q17+q18−q19−4q20−2q21+⋯−3q99+O(q100) q + q^{2} + q^{3} + q^{4} - 4 q^{5} + q^{6} - 2 q^{7} + q^{8} + q^{9} - 4 q^{10} - 3 q^{11} + q^{12} + q^{13} - 2 q^{14} - 4 q^{15} + q^{16} - 7 q^{17} + q^{18} - q^{19} - 4 q^{20} - 2 q^{21}+ \cdots - 3 q^{99}+O(q^{100}) Copy content Toggle raw display

Atkin-Lehner signs

p p Sign
22 −1 -1
33 −1 -1
1313 −1 -1
1919 +1 +1
2929 +1 +1

Inner twists

This newform does not admit any (nontrivial) inner twists.

Twists

Twists of this newform have not been computed.