Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [6023,2,Mod(1,6023)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(6023, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("6023.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 6023 = 19 \cdot 317 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 6023.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: | \(48.0938971374\) |
Analytic rank: | \(1\) |
Dimension: | \(99\) |
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 | −2.79086 | −1.66708 | 5.78891 | 1.47477 | 4.65258 | −1.60538 | −10.5743 | −0.220852 | −4.11587 | ||||||||||||||||||
1.2 | −2.66510 | −2.16013 | 5.10274 | −2.11668 | 5.75694 | −1.28803 | −8.26911 | 1.66614 | 5.64116 | ||||||||||||||||||
1.3 | −2.63080 | −0.151619 | 4.92110 | −0.321250 | 0.398879 | −0.565304 | −7.68484 | −2.97701 | 0.845143 | ||||||||||||||||||
1.4 | −2.62992 | 1.18387 | 4.91650 | 1.04484 | −3.11349 | 0.263404 | −7.67017 | −1.59845 | −2.74784 | ||||||||||||||||||
1.5 | −2.57189 | 2.00338 | 4.61464 | 2.67910 | −5.15249 | −0.0453210 | −6.72459 | 1.01355 | −6.89035 | ||||||||||||||||||
1.6 | −2.56636 | 2.86321 | 4.58620 | −1.49629 | −7.34803 | −1.31440 | −6.63713 | 5.19797 | 3.84001 | ||||||||||||||||||
1.7 | −2.48734 | −0.305991 | 4.18686 | −0.333485 | 0.761103 | 2.33440 | −5.43948 | −2.90637 | 0.829491 | ||||||||||||||||||
1.8 | −2.33180 | −3.18012 | 3.43727 | 0.827568 | 7.41539 | −0.00201560 | −3.35142 | 7.11317 | −1.92972 | ||||||||||||||||||
1.9 | −2.32426 | −2.85691 | 3.40220 | −3.59754 | 6.64022 | −1.30166 | −3.25907 | 5.16196 | 8.36162 | ||||||||||||||||||
1.10 | −2.31886 | 2.08746 | 3.37709 | −2.67469 | −4.84053 | −2.80565 | −3.19328 | 1.35751 | 6.20222 | ||||||||||||||||||
1.11 | −2.31836 | −0.700819 | 3.37481 | −1.53243 | 1.62475 | 2.29352 | −3.18731 | −2.50885 | 3.55272 | ||||||||||||||||||
1.12 | −2.30551 | 2.60917 | 3.31537 | −2.40173 | −6.01546 | 3.07987 | −3.03260 | 3.80775 | 5.53721 | ||||||||||||||||||
1.13 | −2.20989 | −1.74865 | 2.88361 | 1.63174 | 3.86432 | 4.01021 | −1.95267 | 0.0577689 | −3.60597 | ||||||||||||||||||
1.14 | −2.20648 | −1.66546 | 2.86855 | 2.85921 | 3.67480 | −0.996345 | −1.91643 | −0.226251 | −6.30878 | ||||||||||||||||||
1.15 | −2.19313 | 1.00492 | 2.80981 | −2.58247 | −2.20392 | −2.47276 | −1.77602 | −1.99014 | 5.66370 | ||||||||||||||||||
1.16 | −2.15033 | −0.758271 | 2.62390 | −3.61423 | 1.63053 | −3.46519 | −1.34159 | −2.42502 | 7.77178 | ||||||||||||||||||
1.17 | −1.96796 | −0.967508 | 1.87288 | 0.188751 | 1.90402 | −4.91446 | 0.250172 | −2.06393 | −0.371455 | ||||||||||||||||||
1.18 | −1.95928 | 1.09252 | 1.83878 | 1.35010 | −2.14055 | 3.30535 | 0.315883 | −1.80641 | −2.64522 | ||||||||||||||||||
1.19 | −1.90532 | 0.192511 | 1.63023 | 0.483590 | −0.366795 | 3.15438 | 0.704532 | −2.96294 | −0.921392 | ||||||||||||||||||
1.20 | −1.88369 | 2.22834 | 1.54829 | 0.640943 | −4.19751 | −4.86422 | 0.850890 | 1.96551 | −1.20734 | ||||||||||||||||||
See all 99 embeddings |
Atkin-Lehner signs
\( p \) | Sign |
---|---|
\(19\) | \(1\) |
\(317\) | \(1\) |
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 | 6023.2.a.b | ✓ | 99 |
By twisted newform orbit | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Mult | Type |
6023.2.a.b | ✓ | 99 | 1.a | even | 1 | 1 | trivial |