Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [983,6,Mod(1,983)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
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")
//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: | \( N \) | \(=\) | \( 983 \) |
Weight: | \( k \) | \(=\) | \( 6 \) |
Character orbit: | \([\chi]\) | \(=\) | 983.a (trivial) |
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: | yes |
Analytic conductor: | \(157.657294876\) |
Analytic rank: | \(0\) |
Dimension: | \(218\) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
$q$-expansion
The algebraic \(q\)-expansion of this newform has not been computed, but we have computed the trace expansion.
Embeddings
For each embedding \(\iota_m\) of the coefficient field, the values \(\iota_m(a_n)\) 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 | \( a_{2} \) | \( a_{3} \) | \( a_{4} \) | \( a_{5} \) | \( a_{6} \) | \( a_{7} \) | \( a_{8} \) | \( a_{9} \) | \( a_{10} \) | ||||||||||||||||||
---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
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) |
Atkin-Lehner signs
\( p \) | Sign |
---|---|
\(983\) | \( -1 \) |
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 |