Properties

Label 983.6.a.b
Level 983983
Weight 66
Character orbit 983.a
Self dual yes
Analytic conductor 157.657157.657
Analytic rank 00
Dimension 218218
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] = [983,6,Mod(1,983)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)
 
Copy content sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(983, base_ring=CyclotomicField(2)) chi = DirichletCharacter(H, H._module([0])) N = Newforms(chi, 6, names="a")
 
Copy content magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("983.1"); S:= CuspForms(chi, 6); N := Newforms(S);
 
Level: N N == 983 983
Weight: k k == 6 6
Character orbit: [χ][\chi] == 983.a (trivial)

Newform invariants

Copy content comment:select newform
 
Copy content sage:traces = [218] 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: yes
Analytic conductor: 157.657294876157.657294876
Analytic rank: 00
Dimension: 218218
Twist minimal: yes
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) = 218q+35q2+70q3+3685q4+253q5+529q6+1567q7+1695q8+19812q9+2133q10+1752q11+3512q12+5990q13+2319q14+4639q15+66105q16++627643q99+O(q100) 218 q + 35 q^{2} + 70 q^{3} + 3685 q^{4} + 253 q^{5} + 529 q^{6} + 1567 q^{7} + 1695 q^{8} + 19812 q^{9} + 2133 q^{10} + 1752 q^{11} + 3512 q^{12} + 5990 q^{13} + 2319 q^{14} + 4639 q^{15} + 66105 q^{16}+ \cdots + 627643 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}
1.1 −11.2545 14.3637 94.6632 5.42124 −161.655 48.2201 −705.242 −36.6855 −61.0132
1.2 −11.0647 −25.4268 90.4285 75.4706 281.341 155.090 −646.496 403.521 −835.063
1.3 −11.0396 −16.6850 89.8732 −54.0018 184.196 −10.8436 −638.898 35.3900 596.159
1.4 −11.0108 −2.28470 89.2387 53.2861 25.1565 −155.822 −630.246 −237.780 −586.724
1.5 −11.0085 27.1723 89.1872 −88.2795 −299.126 52.5145 −629.545 495.333 971.825
1.6 −10.8442 −6.29114 85.5966 9.46707 68.2223 −20.0151 −581.212 −203.422 −102.663
1.7 −10.7977 −15.2978 84.5913 −106.934 165.182 232.255 −567.867 −8.97689 1154.65
1.8 −10.7909 23.9514 84.4434 90.3849 −258.457 150.379 −565.911 330.669 −975.334
1.9 −10.6923 3.77147 82.3260 −15.6343 −40.3258 194.820 −538.102 −228.776 167.167
1.10 −10.6888 −2.78158 82.2511 63.0885 29.7318 −133.230 −537.126 −235.263 −674.342
1.11 −10.4420 0.0889574 77.0361 −100.525 −0.928896 31.6163 −470.268 −242.992 1049.69
1.12 −10.3513 9.89991 75.1501 97.3083 −102.477 −91.6942 −446.662 −144.992 −1007.27
1.13 −10.1039 11.1728 70.0889 83.9898 −112.889 92.1063 −384.847 −118.168 −848.625
1.14 −10.0849 8.47019 69.7046 6.04415 −85.4208 −170.780 −380.247 −171.256 −60.9545
1.15 −10.0174 −24.0669 68.3476 39.3861 241.087 −242.470 −364.107 336.214 −394.545
1.16 −9.86337 −14.1514 65.2861 8.97631 139.581 −99.2905 −328.313 −42.7375 −88.5367
1.17 −9.77516 −29.0216 63.5537 −38.6585 283.690 235.286 −308.442 599.250 377.893
1.18 −9.74643 22.6936 62.9930 3.05529 −221.181 −41.0311 −302.071 271.998 −29.7782
1.19 −9.67677 −17.9132 61.6399 −79.1572 173.342 −217.764 −286.818 77.8823 765.986
1.20 −9.61332 27.9669 60.4159 −41.3834 −268.854 221.300 −273.171 539.145 397.832
See next 80 embeddings (of 218 total)
nn: e.g. 2-40 or 990-1000
Embeddings: e.g. 1-3 or 1.218
Significant digits:
Format:

Atkin-Lehner signs

p p Sign
983983 1 -1

Inner twists

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

Twists

       By twisting character orbit
Char Parity Ord Mult Type Twist Min Dim
1.a even 1 1 trivial 983.6.a.b 218
    
        By twisted newform orbit
Twist Min Dim Char Parity Ord Mult Type
983.6.a.b 218 1.a even 1 1 trivial