Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [4019,2,Mod(1,4019)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(4019, 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("4019.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 4019 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 4019.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: | \(32.0918765724\) |
Analytic rank: | \(0\) |
Dimension: | \(186\) |
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 | −2.80607 | −1.31751 | 5.87400 | −0.399238 | 3.69703 | −2.36747 | −10.8707 | −1.26416 | 1.12029 | ||||||||||||||||||
1.2 | −2.79148 | −3.39321 | 5.79236 | 3.31167 | 9.47208 | −0.0588258 | −10.5863 | 8.51387 | −9.24445 | ||||||||||||||||||
1.3 | −2.78390 | 2.40470 | 5.75012 | −2.23828 | −6.69445 | −0.0567746 | −10.4400 | 2.78257 | 6.23116 | ||||||||||||||||||
1.4 | −2.77200 | −0.494167 | 5.68400 | 0.905775 | 1.36983 | 1.77801 | −10.2121 | −2.75580 | −2.51081 | ||||||||||||||||||
1.5 | −2.72152 | −2.92759 | 5.40665 | −3.58721 | 7.96750 | −4.23646 | −9.27126 | 5.57081 | 9.76265 | ||||||||||||||||||
1.6 | −2.71067 | −2.48956 | 5.34775 | −1.96358 | 6.74838 | 3.14635 | −9.07467 | 3.19790 | 5.32263 | ||||||||||||||||||
1.7 | −2.69011 | 0.353602 | 5.23670 | −0.999886 | −0.951229 | 3.25121 | −8.70707 | −2.87497 | 2.68981 | ||||||||||||||||||
1.8 | −2.67918 | 1.79491 | 5.17799 | 3.40719 | −4.80888 | 4.24264 | −8.51439 | 0.221695 | −9.12846 | ||||||||||||||||||
1.9 | −2.62160 | −1.74677 | 4.87277 | −3.59409 | 4.57932 | 5.00470 | −7.53124 | 0.0512031 | 9.42226 | ||||||||||||||||||
1.10 | −2.60285 | −0.581840 | 4.77483 | 3.23074 | 1.51444 | −2.22687 | −7.22248 | −2.66146 | −8.40914 | ||||||||||||||||||
1.11 | −2.59341 | 1.69325 | 4.72575 | −3.22826 | −4.39129 | −0.750732 | −7.06898 | −0.132895 | 8.37219 | ||||||||||||||||||
1.12 | −2.56992 | −0.512548 | 4.60446 | −4.01178 | 1.31721 | 0.174790 | −6.69325 | −2.73729 | 10.3099 | ||||||||||||||||||
1.13 | −2.56492 | −2.35383 | 4.57881 | 1.72936 | 6.03739 | −3.13382 | −6.61443 | 2.54053 | −4.43566 | ||||||||||||||||||
1.14 | −2.55030 | 3.02512 | 4.50404 | −1.05624 | −7.71496 | 5.05580 | −6.38607 | 6.15132 | 2.69374 | ||||||||||||||||||
1.15 | −2.52937 | 0.978887 | 4.39770 | −0.161932 | −2.47596 | −2.77531 | −6.06468 | −2.04178 | 0.409586 | ||||||||||||||||||
1.16 | −2.43886 | −0.628245 | 3.94805 | 3.87591 | 1.53220 | −4.09962 | −4.75103 | −2.60531 | −9.45281 | ||||||||||||||||||
1.17 | −2.43453 | 2.49356 | 3.92696 | 3.69129 | −6.07065 | 0.601351 | −4.69125 | 3.21782 | −8.98658 | ||||||||||||||||||
1.18 | −2.40616 | −0.556574 | 3.78961 | 1.68267 | 1.33921 | 2.28423 | −4.30608 | −2.69023 | −4.04878 | ||||||||||||||||||
1.19 | −2.39579 | 3.13150 | 3.73980 | 0.529965 | −7.50242 | −1.46029 | −4.16820 | 6.80631 | −1.26968 | ||||||||||||||||||
1.20 | −2.34165 | −0.437788 | 3.48332 | 0.358726 | 1.02515 | 3.39349 | −3.47342 | −2.80834 | −0.840010 | ||||||||||||||||||
See next 80 embeddings (of 186 total) |
Atkin-Lehner signs
\( p \) | Sign |
---|---|
\(4019\) | \(-1\) |
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 | 4019.2.a.b | ✓ | 186 |
By twisted newform orbit | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Mult | Type |
4019.2.a.b | ✓ | 186 | 1.a | even | 1 | 1 | trivial |