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: | \(98\) |
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 | −2.78159 | 0.980083 | 5.73723 | −2.26646 | −2.72619 | 0.130985 | −10.3954 | −2.03944 | 6.30436 | ||||||||||||||||||
1.2 | −2.72324 | −3.03839 | 5.41603 | −0.824121 | 8.27426 | −3.50609 | −9.30267 | 6.23182 | 2.24428 | ||||||||||||||||||
1.3 | −2.72317 | −0.516928 | 5.41568 | 3.12322 | 1.40769 | −3.06631 | −9.30149 | −2.73279 | −8.50508 | ||||||||||||||||||
1.4 | −2.63244 | −2.81028 | 4.92974 | 1.41252 | 7.39789 | 3.18061 | −7.71236 | 4.89767 | −3.71838 | ||||||||||||||||||
1.5 | −2.52650 | 1.56416 | 4.38319 | 1.08994 | −3.95184 | 4.94624 | −6.02111 | −0.553409 | −2.75372 | ||||||||||||||||||
1.6 | −2.52400 | −0.270526 | 4.37060 | −2.19505 | 0.682808 | −4.06184 | −5.98340 | −2.92682 | 5.54031 | ||||||||||||||||||
1.7 | −2.51733 | −2.83375 | 4.33693 | 3.33686 | 7.13347 | 2.06105 | −5.88281 | 5.03014 | −8.39997 | ||||||||||||||||||
1.8 | −2.51387 | −0.144321 | 4.31953 | 2.01567 | 0.362803 | 1.13174 | −5.83100 | −2.97917 | −5.06713 | ||||||||||||||||||
1.9 | −2.51046 | 3.07291 | 4.30243 | 0.528149 | −7.71443 | −0.975247 | −5.78017 | 6.44278 | −1.32590 | ||||||||||||||||||
1.10 | −2.36387 | −1.85446 | 3.58790 | −2.76467 | 4.38371 | 3.05083 | −3.75360 | 0.439017 | 6.53534 | ||||||||||||||||||
1.11 | −2.30301 | −0.172789 | 3.30385 | −0.809544 | 0.397934 | 0.778568 | −3.00278 | −2.97014 | 1.86439 | ||||||||||||||||||
1.12 | −2.23585 | 2.07159 | 2.99900 | 2.91944 | −4.63176 | −1.89696 | −2.23362 | 1.29150 | −6.52741 | ||||||||||||||||||
1.13 | −2.22980 | 2.83472 | 2.97200 | −0.749386 | −6.32084 | 0.730492 | −2.16735 | 5.03561 | 1.67098 | ||||||||||||||||||
1.14 | −2.16233 | −1.79610 | 2.67567 | −1.92302 | 3.88377 | 3.63289 | −1.46101 | 0.225992 | 4.15820 | ||||||||||||||||||
1.15 | −2.15437 | −1.80294 | 2.64131 | 1.24504 | 3.88420 | −4.16426 | −1.38162 | 0.250590 | −2.68227 | ||||||||||||||||||
1.16 | −2.11992 | 0.896090 | 2.49404 | 2.73729 | −1.89963 | −3.12431 | −1.04733 | −2.19702 | −5.80282 | ||||||||||||||||||
1.17 | −2.03453 | −2.81750 | 2.13929 | −2.44691 | 5.73228 | −2.76718 | −0.283395 | 4.93833 | 4.97829 | ||||||||||||||||||
1.18 | −2.01585 | 1.02156 | 2.06364 | 0.907276 | −2.05931 | 1.44669 | −0.128285 | −1.95642 | −1.82893 | ||||||||||||||||||
1.19 | −1.95295 | 2.01904 | 1.81400 | −3.44278 | −3.94307 | −1.14802 | 0.363246 | 1.07651 | 6.72357 | ||||||||||||||||||
1.20 | −1.88657 | −2.34604 | 1.55916 | 1.12157 | 4.42598 | 2.57604 | 0.831673 | 2.50392 | −2.11593 | ||||||||||||||||||
See all 98 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.a | ✓ | 98 |
By twisted newform orbit | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Mult | Type |
6023.2.a.a | ✓ | 98 | 1.a | even | 1 | 1 | trivial |