Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [983,4,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, 4, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("983.1");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 983 \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
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: | \(57.9988775356\) |
Analytic rank: | \(1\) |
Dimension: | \(109\) |
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 | −5.58646 | −0.724275 | 23.2085 | 15.1603 | 4.04613 | 11.0308 | −84.9620 | −26.4754 | −84.6926 | ||||||||||||||||||
1.2 | −5.43981 | −4.19474 | 21.5915 | −1.69960 | 22.8186 | −29.9614 | −73.9355 | −9.40415 | 9.24553 | ||||||||||||||||||
1.3 | −5.36058 | −0.495047 | 20.7358 | −12.0516 | 2.65374 | −0.578955 | −68.2712 | −26.7549 | 64.6036 | ||||||||||||||||||
1.4 | −5.35691 | −6.65704 | 20.6965 | 16.4748 | 35.6612 | −32.9904 | −68.0141 | 17.3161 | −88.2542 | ||||||||||||||||||
1.5 | −5.26153 | −9.03263 | 19.6837 | −5.00636 | 47.5254 | 5.47420 | −61.4739 | 54.5884 | 26.3411 | ||||||||||||||||||
1.6 | −5.25670 | 8.92364 | 19.6329 | −14.6619 | −46.9089 | −4.44244 | −61.1508 | 52.6313 | 77.0735 | ||||||||||||||||||
1.7 | −5.11709 | 4.98154 | 18.1846 | 19.4669 | −25.4910 | −11.1023 | −52.1157 | −2.18425 | −99.6141 | ||||||||||||||||||
1.8 | −4.98778 | 3.08939 | 16.8780 | 10.2056 | −15.4092 | 13.1728 | −44.2815 | −17.4557 | −50.9035 | ||||||||||||||||||
1.9 | −4.84438 | −3.38875 | 15.4680 | 9.70346 | 16.4164 | −1.30349 | −36.1777 | −15.5163 | −47.0072 | ||||||||||||||||||
1.10 | −4.76983 | 4.01927 | 14.7512 | −2.78342 | −19.1712 | 17.1208 | −32.2023 | −10.8454 | 13.2764 | ||||||||||||||||||
1.11 | −4.76719 | 8.84156 | 14.7261 | −7.92466 | −42.1494 | −15.4085 | −32.0645 | 51.1732 | 37.7783 | ||||||||||||||||||
1.12 | −4.74560 | 9.89469 | 14.5207 | 10.6639 | −46.9563 | −4.53278 | −30.9447 | 70.9049 | −50.6066 | ||||||||||||||||||
1.13 | −4.67338 | 5.53617 | 13.8405 | −1.05395 | −25.8727 | 16.9979 | −27.2950 | 3.64920 | 4.92552 | ||||||||||||||||||
1.14 | −4.63586 | −1.39484 | 13.4912 | −1.90865 | 6.46628 | −14.9064 | −25.4564 | −25.0544 | 8.84822 | ||||||||||||||||||
1.15 | −4.54428 | −2.38245 | 12.6505 | −17.0184 | 10.8265 | −0.746020 | −21.1331 | −21.3239 | 77.3363 | ||||||||||||||||||
1.16 | −4.46204 | −5.70729 | 11.9098 | −10.3218 | 25.4662 | 32.8198 | −17.4456 | 5.57321 | 46.0562 | ||||||||||||||||||
1.17 | −4.42678 | −9.72553 | 11.5964 | −7.04425 | 43.0527 | −25.6819 | −15.9203 | 67.5859 | 31.1833 | ||||||||||||||||||
1.18 | −4.32365 | 6.42278 | 10.6939 | 0.242187 | −27.7698 | 13.8062 | −11.6476 | 14.2521 | −1.04713 | ||||||||||||||||||
1.19 | −4.23489 | 5.14870 | 9.93428 | −19.0899 | −21.8042 | −26.8153 | −8.19147 | −0.490926 | 80.8438 | ||||||||||||||||||
1.20 | −4.06969 | −3.69076 | 8.56235 | −18.1705 | 15.0202 | −23.3834 | −2.28858 | −13.3783 | 73.9482 | ||||||||||||||||||
See next 80 embeddings (of 109 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 | 983.4.a.a | ✓ | 109 |
By twisted newform orbit | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Mult | Type |
983.4.a.a | ✓ | 109 | 1.a | even | 1 | 1 | trivial |