Properties

Label 532.2.k.b
Level 532532
Weight 22
Character orbit 532.k
Analytic conductor 4.2484.248
Analytic rank 00
Dimension 2424
Inner twists 22

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Newspace parameters

Copy content comment:Compute space of new eigenforms
 
Copy content gp:[N,k,chi] = [532,2,Mod(121,532)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)
 
Copy content sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(532, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([0, 2, 2])) 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("532.121"); S:= CuspForms(chi, 2); N := Newforms(S);
 
Level: N N == 532=22719 532 = 2^{2} \cdot 7 \cdot 19
Weight: k k == 2 2
Character orbit: [χ][\chi] == 532.k (of order 33, degree 22, minimal)

Newform invariants

Copy content comment:select newform
 
Copy content sage:traces = [24] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(1)] == traces)
 
Copy content gp:f = lf[1] \\ Warning: the index may be different
 
Self dual: no
Analytic conductor: 4.248041387534.24804138753
Analytic rank: 00
Dimension: 2424
Relative dimension: 1212 over Q(ζ3)\Q(\zeta_{3})
Twist minimal: yes
Sato-Tate group: SU(2)[C3]\mathrm{SU}(2)[C_{3}]

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) = 24qq3+12q56q715q9+q117q132q15+3q1719q19+12q21+8q23+16q25+20q2722q297q3114q33+18q35+9q37+27q99+O(q100) 24 q - q^{3} + 12 q^{5} - 6 q^{7} - 15 q^{9} + q^{11} - 7 q^{13} - 2 q^{15} + 3 q^{17} - 19 q^{19} + 12 q^{21} + 8 q^{23} + 16 q^{25} + 20 q^{27} - 22 q^{29} - 7 q^{31} - 14 q^{33} + 18 q^{35} + 9 q^{37}+ \cdots - 27 q^{99}+O(q^{100}) Copy content Toggle raw display

Embeddings

For each embedding ιm\iota_m of the coefficient field, the values ιm(an)\iota_m(a_n) are shown below.

For more information on an embedded modular form you can click on its label.

Copy content comment:embeddings in the coefficient field
 
Copy content gp:mfembed(f)
 
Label   a2 a_{2} a3 a_{3} a4 a_{4} a5 a_{5} a6 a_{6} a7 a_{7} a8 a_{8} a9 a_{9} a10 a_{10}
121.1 0 −1.66499 + 2.88385i 0 2.17686 0 −2.16805 1.51643i 0 −4.04441 7.00512i 0
121.2 0 −1.49182 + 2.58391i 0 0.446078 0 1.18643 + 2.36482i 0 −2.95105 5.11136i 0
121.3 0 −1.00455 + 1.73993i 0 −0.208844 0 0.452777 2.60672i 0 −0.518227 0.897596i 0
121.4 0 −0.771712 + 1.33665i 0 −2.99584 0 −2.55868 + 0.673181i 0 0.308920 + 0.535065i 0
121.5 0 −0.520631 + 0.901759i 0 3.47279 0 2.62969 + 0.291052i 0 0.957887 + 1.65911i 0
121.6 0 −0.0989313 + 0.171354i 0 2.23136 0 −1.27819 2.31651i 0 1.48043 + 2.56417i 0
121.7 0 0.0144506 0.0250292i 0 −0.520300 0 −2.55086 + 0.702209i 0 1.49958 + 2.59735i 0
121.8 0 0.536703 0.929597i 0 3.52186 0 −1.25747 + 2.32783i 0 0.923900 + 1.60024i 0
121.9 0 0.609809 1.05622i 0 −3.23495 0 1.15617 + 2.37976i 0 0.756266 + 1.30989i 0
121.10 0 1.02695 1.77872i 0 −2.32366 0 −0.804015 2.52063i 0 −0.609239 1.05523i 0
121.11 0 1.27630 2.21062i 0 0.584291 0 0.854338 + 2.50402i 0 −1.75791 3.04478i 0
121.12 0 1.58842 2.75122i 0 2.85036 0 1.33785 2.28258i 0 −3.54616 6.14212i 0
277.1 0 −1.66499 2.88385i 0 2.17686 0 −2.16805 + 1.51643i 0 −4.04441 + 7.00512i 0
277.2 0 −1.49182 2.58391i 0 0.446078 0 1.18643 2.36482i 0 −2.95105 + 5.11136i 0
277.3 0 −1.00455 1.73993i 0 −0.208844 0 0.452777 + 2.60672i 0 −0.518227 + 0.897596i 0
277.4 0 −0.771712 1.33665i 0 −2.99584 0 −2.55868 0.673181i 0 0.308920 0.535065i 0
277.5 0 −0.520631 0.901759i 0 3.47279 0 2.62969 0.291052i 0 0.957887 1.65911i 0
277.6 0 −0.0989313 0.171354i 0 2.23136 0 −1.27819 + 2.31651i 0 1.48043 2.56417i 0
277.7 0 0.0144506 + 0.0250292i 0 −0.520300 0 −2.55086 0.702209i 0 1.49958 2.59735i 0
277.8 0 0.536703 + 0.929597i 0 3.52186 0 −1.25747 2.32783i 0 0.923900 1.60024i 0
See all 24 embeddings
nn: e.g. 2-40 or 990-1000
Embeddings: e.g. 1-3 or 121.12
Significant digits:
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Inner twists

Char Parity Ord Mult Type
1.a even 1 1 trivial
133.h even 3 1 inner

Twists

       By twisting character orbit
Char Parity Ord Mult Type Twist Min Dim
1.a even 1 1 trivial 532.2.k.b 24
7.c even 3 1 532.2.l.b yes 24
19.c even 3 1 532.2.l.b yes 24
133.h even 3 1 inner 532.2.k.b 24
    
        By twisted newform orbit
Twist Min Dim Char Parity Ord Mult Type
532.2.k.b 24 1.a even 1 1 trivial
532.2.k.b 24 133.h even 3 1 inner
532.2.l.b yes 24 7.c even 3 1
532.2.l.b yes 24 19.c even 3 1

Hecke kernels

This newform subspace can be constructed as the kernel of the linear operator T324+T323+26T322+15T321+425T320+193T319+4117T318++16 T_{3}^{24} + T_{3}^{23} + 26 T_{3}^{22} + 15 T_{3}^{21} + 425 T_{3}^{20} + 193 T_{3}^{19} + 4117 T_{3}^{18} + \cdots + 16 acting on S2new(532,[χ])S_{2}^{\mathrm{new}}(532, [\chi]). Copy content Toggle raw display