Properties

Label 42978.2.a.t
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 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")
 
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);
 
Level: N N == 42978=23131929 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,-1,1,-5,1,1,-1,-6,1,1,-5,-1,1,-4,1,-1,-1,-5,-6,-3,1, -4,1,1,-5,-1,-1,0,1,-6,-4,5,1,-5,-1,1,-1,-8,-5,-10,-6,-1,-3,12,1,18,-4, -4,1,-11,1,6,-5,-1,-1,-11,-1,-5,0,-5,1,-1,-6,2,-4,-3,5,-9,1,-16,-5,-4, -1,30,1,-13,-1,1,-8,12,-5,4,-10,-1,-6,6,-1,-5,-3,0,12,1,1,13,18,-6,-4] 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+q4q5+q65q7+q8+q9q106q11+q12+q135q14q15+q164q17+q18q19q205q216q22+6q99+O(q100) q + q^{2} + q^{3} + q^{4} - q^{5} + q^{6} - 5 q^{7} + q^{8} + q^{9} - q^{10} - 6 q^{11} + q^{12} + q^{13} - 5 q^{14} - q^{15} + q^{16} - 4 q^{17} + q^{18} - q^{19} - q^{20} - 5 q^{21} - 6 q^{22}+ \cdots - 6 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.