Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [983,2,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, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("983.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 983 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
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: | \(7.84929451869\) |
Analytic rank: | \(0\) |
Dimension: | \(54\) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
$q$-expansion
The dimension is sufficiently large that we do not compute an algebraic \(q\)-expansion, 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 | −2.79902 | −1.37741 | 5.83449 | −1.52700 | 3.85540 | 4.50391 | −10.7328 | −1.10273 | 4.27409 | ||||||||||||||||||
1.2 | −2.59593 | −0.548664 | 4.73883 | 3.85051 | 1.42429 | −1.35607 | −7.10979 | −2.69897 | −9.99563 | ||||||||||||||||||
1.3 | −2.56280 | 2.68242 | 4.56793 | 0.599683 | −6.87450 | 3.67314 | −6.58109 | 4.19537 | −1.53687 | ||||||||||||||||||
1.4 | −2.55366 | 2.02223 | 4.52118 | −4.30555 | −5.16409 | 1.54441 | −6.43825 | 1.08942 | 10.9949 | ||||||||||||||||||
1.5 | −2.42129 | 0.803744 | 3.86265 | 3.28925 | −1.94610 | 3.29937 | −4.51003 | −2.35400 | −7.96423 | ||||||||||||||||||
1.6 | −2.36689 | −1.50082 | 3.60219 | −1.85949 | 3.55227 | 0.0863179 | −3.79222 | −0.747553 | 4.40121 | ||||||||||||||||||
1.7 | −2.28382 | 1.07395 | 3.21585 | −3.29381 | −2.45272 | −2.40396 | −2.77679 | −1.84662 | 7.52248 | ||||||||||||||||||
1.8 | −2.11673 | −3.41526 | 2.48055 | −2.85207 | 7.22918 | 3.49572 | −1.01719 | 8.66400 | 6.03706 | ||||||||||||||||||
1.9 | −2.08433 | 3.17224 | 2.34444 | 0.336118 | −6.61201 | −1.75412 | −0.717929 | 7.06313 | −0.700583 | ||||||||||||||||||
1.10 | −1.83512 | −2.37856 | 1.36768 | −0.131265 | 4.36496 | −4.16934 | 1.16038 | 2.65756 | 0.240888 | ||||||||||||||||||
1.11 | −1.70929 | −2.85036 | 0.921666 | 3.70678 | 4.87208 | −1.37276 | 1.84318 | 5.12455 | −6.33595 | ||||||||||||||||||
1.12 | −1.58618 | −1.33638 | 0.515976 | 0.931296 | 2.11975 | 2.81580 | 2.35393 | −1.21408 | −1.47721 | ||||||||||||||||||
1.13 | −1.55013 | −0.251970 | 0.402914 | −1.29975 | 0.390586 | −4.11447 | 2.47570 | −2.93651 | 2.01479 | ||||||||||||||||||
1.14 | −1.53339 | 2.66681 | 0.351281 | 4.12109 | −4.08926 | 2.92035 | 2.52813 | 4.11188 | −6.31924 | ||||||||||||||||||
1.15 | −1.45073 | 1.34954 | 0.104610 | 3.00144 | −1.95782 | −1.88776 | 2.74969 | −1.17873 | −4.35427 | ||||||||||||||||||
1.16 | −1.39657 | 1.31114 | −0.0496049 | −1.59833 | −1.83110 | 4.09968 | 2.86241 | −1.28090 | 2.23217 | ||||||||||||||||||
1.17 | −1.13542 | −1.73773 | −0.710827 | −4.00726 | 1.97305 | 3.34589 | 3.07792 | 0.0197210 | 4.54991 | ||||||||||||||||||
1.18 | −1.00569 | −0.156806 | −0.988591 | 0.630600 | 0.157698 | −3.47391 | 3.00559 | −2.97541 | −0.634187 | ||||||||||||||||||
1.19 | −0.870233 | −2.53615 | −1.24269 | 1.03445 | 2.20704 | 5.14837 | 2.82190 | 3.43208 | −0.900213 | ||||||||||||||||||
1.20 | −0.773901 | 2.93267 | −1.40108 | 2.13834 | −2.26960 | 2.57212 | 2.63210 | 5.60055 | −1.65486 | ||||||||||||||||||
See all 54 embeddings |
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 | 983.2.a.b | ✓ | 54 |
3.b | odd | 2 | 1 | 8847.2.a.g | 54 |
By twisted newform orbit | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Mult | Type |
983.2.a.b | ✓ | 54 | 1.a | even | 1 | 1 | trivial |
8847.2.a.g | 54 | 3.b | odd | 2 | 1 |
Hecke kernels
This newform subspace can be constructed as the kernel of the linear operator \( T_{2}^{54} - 8 T_{2}^{53} - 54 T_{2}^{52} + 584 T_{2}^{51} + 1042 T_{2}^{50} - 19796 T_{2}^{49} + \cdots - 983 \) acting on \(S_{2}^{\mathrm{new}}(\Gamma_0(983))\).