Properties

Label 936.2.dr.b
Level 936936
Weight 22
Character orbit 936.dr
Analytic conductor 7.4747.474
Analytic rank 00
Dimension 3232
Inner twists 44

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [936,2,Mod(89,936)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(936, base_ring=CyclotomicField(12))
 
chi = DirichletCharacter(H, H._module([0, 0, 6, 7]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("936.89");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: N N == 936=233213 936 = 2^{3} \cdot 3^{2} \cdot 13
Weight: k k == 2 2
Character orbit: [χ][\chi] == 936.dr (of order 1212, degree 44, minimal)

Newform invariants

comment: select newform
 
sage: f = N[0] # Warning: the index may be different
 
gp: f = lf[1] \\ Warning: the index may be different
 
Self dual: no
Analytic conductor: 7.473997629197.47399762919
Analytic rank: 00
Dimension: 3232
Relative dimension: 88 over Q(ζ12)\Q(\zeta_{12})
Twist minimal: yes
Sato-Tate group: SU(2)[C12]\mathrm{SU}(2)[C_{12}]

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) = 32q+4q720q134q19+4q31+60q43+84q4928q6124q67+16q73+48q79+88q85116q91+72q97+O(q100) 32 q + 4 q^{7} - 20 q^{13} - 4 q^{19} + 4 q^{31} + 60 q^{43} + 84 q^{49} - 28 q^{61} - 24 q^{67} + 16 q^{73} + 48 q^{79} + 88 q^{85} - 116 q^{91} + 72 q^{97}+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.

comment: embeddings in the coefficient field
 
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}
89.1 0 0 0 −2.43408 + 2.43408i 0 −0.0623138 0.232558i 0 0 0
89.2 0 0 0 −1.84163 + 1.84163i 0 −0.618766 2.30927i 0 0 0
89.3 0 0 0 −1.79153 + 1.79153i 0 1.02710 + 3.83317i 0 0 0
89.4 0 0 0 −0.491974 + 0.491974i 0 0.153985 + 0.574679i 0 0 0
89.5 0 0 0 0.491974 0.491974i 0 0.153985 + 0.574679i 0 0 0
89.6 0 0 0 1.79153 1.79153i 0 1.02710 + 3.83317i 0 0 0
89.7 0 0 0 1.84163 1.84163i 0 −0.618766 2.30927i 0 0 0
89.8 0 0 0 2.43408 2.43408i 0 −0.0623138 0.232558i 0 0 0
305.1 0 0 0 −2.43408 2.43408i 0 −0.0623138 + 0.232558i 0 0 0
305.2 0 0 0 −1.84163 1.84163i 0 −0.618766 + 2.30927i 0 0 0
305.3 0 0 0 −1.79153 1.79153i 0 1.02710 3.83317i 0 0 0
305.4 0 0 0 −0.491974 0.491974i 0 0.153985 0.574679i 0 0 0
305.5 0 0 0 0.491974 + 0.491974i 0 0.153985 0.574679i 0 0 0
305.6 0 0 0 1.79153 + 1.79153i 0 1.02710 3.83317i 0 0 0
305.7 0 0 0 1.84163 + 1.84163i 0 −0.618766 + 2.30927i 0 0 0
305.8 0 0 0 2.43408 + 2.43408i 0 −0.0623138 + 0.232558i 0 0 0
449.1 0 0 0 −2.65632 + 2.65632i 0 1.47941 + 0.396406i 0 0 0
449.2 0 0 0 −2.57811 + 2.57811i 0 −3.04951 0.817113i 0 0 0
449.3 0 0 0 −1.44645 + 1.44645i 0 4.86936 + 1.30474i 0 0 0
449.4 0 0 0 −0.661135 + 0.661135i 0 −2.79926 0.750059i 0 0 0
See all 32 embeddings
nn: e.g. 2-40 or 990-1000
Embeddings: e.g. 1-3 or 89.8
Significant digits:
Format:

Inner twists

Char Parity Ord Mult Type
1.a even 1 1 trivial
3.b odd 2 1 inner
13.f odd 12 1 inner
39.k even 12 1 inner

Twists

       By twisting character orbit
Char Parity Ord Mult Type Twist Min Dim
1.a even 1 1 trivial 936.2.dr.b 32
3.b odd 2 1 inner 936.2.dr.b 32
13.f odd 12 1 inner 936.2.dr.b 32
39.k even 12 1 inner 936.2.dr.b 32
    
        By twisted newform orbit
Twist Min Dim Char Parity Ord Mult Type
936.2.dr.b 32 1.a even 1 1 trivial
936.2.dr.b 32 3.b odd 2 1 inner
936.2.dr.b 32 13.f odd 12 1 inner
936.2.dr.b 32 39.k even 12 1 inner

Hecke kernels

This newform subspace can be constructed as the kernel of the linear operator T532+622T528+146079T524+16099804T520+851715007T516++29376588816 T_{5}^{32} + 622 T_{5}^{28} + 146079 T_{5}^{24} + 16099804 T_{5}^{20} + 851715007 T_{5}^{16} + \cdots + 29376588816 acting on S2new(936,[χ])S_{2}^{\mathrm{new}}(936, [\chi]). Copy content Toggle raw display