Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [8029,2,Mod(1,8029)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(8029, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 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("8029.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 8029 = 7 \cdot 31 \cdot 37 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 8029.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: | \(64.1118877829\) |
Analytic rank: | \(1\) |
Dimension: | \(64\) |
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 | −2.78373 | −1.87011 | 5.74916 | 1.28741 | 5.20588 | 1.00000 | −10.4367 | 0.497300 | −3.58380 | ||||||||||||||||||
1.2 | −2.73543 | 2.30900 | 5.48259 | −0.479374 | −6.31610 | 1.00000 | −9.52639 | 2.33146 | 1.31130 | ||||||||||||||||||
1.3 | −2.60868 | 1.74395 | 4.80524 | 3.41549 | −4.54942 | 1.00000 | −7.31797 | 0.0413660 | −8.90994 | ||||||||||||||||||
1.4 | −2.55819 | −1.74755 | 4.54434 | −3.94326 | 4.47057 | 1.00000 | −6.50890 | 0.0539426 | 10.0876 | ||||||||||||||||||
1.5 | −2.54725 | −0.119258 | 4.48849 | −2.50621 | 0.303779 | 1.00000 | −6.33880 | −2.98578 | 6.38394 | ||||||||||||||||||
1.6 | −2.47744 | −3.01159 | 4.13771 | −1.82686 | 7.46104 | 1.00000 | −5.29605 | 6.06970 | 4.52594 | ||||||||||||||||||
1.7 | −2.36739 | 2.20020 | 3.60455 | −3.91478 | −5.20875 | 1.00000 | −3.79861 | 1.84090 | 9.26783 | ||||||||||||||||||
1.8 | −2.29578 | 1.37707 | 3.27061 | 1.05070 | −3.16145 | 1.00000 | −2.91703 | −1.10368 | −2.41218 | ||||||||||||||||||
1.9 | −2.23247 | 0.196842 | 2.98394 | −3.18984 | −0.439445 | 1.00000 | −2.19661 | −2.96125 | 7.12122 | ||||||||||||||||||
1.10 | −2.05832 | −2.27198 | 2.23670 | 1.17054 | 4.67648 | 1.00000 | −0.487203 | 2.16191 | −2.40935 | ||||||||||||||||||
1.11 | −1.98856 | 1.88562 | 1.95439 | 2.26240 | −3.74968 | 1.00000 | 0.0906987 | 0.555562 | −4.49892 | ||||||||||||||||||
1.12 | −1.97375 | 0.623779 | 1.89568 | −0.759767 | −1.23118 | 1.00000 | 0.205897 | −2.61090 | 1.49959 | ||||||||||||||||||
1.13 | −1.82754 | −3.16895 | 1.33992 | 3.82020 | 5.79139 | 1.00000 | 1.20633 | 7.04224 | −6.98159 | ||||||||||||||||||
1.14 | −1.82638 | −2.11005 | 1.33567 | 1.69503 | 3.85376 | 1.00000 | 1.21333 | 1.45233 | −3.09578 | ||||||||||||||||||
1.15 | −1.77753 | 3.13869 | 1.15960 | −1.45610 | −5.57910 | 1.00000 | 1.49384 | 6.85138 | 2.58826 | ||||||||||||||||||
1.16 | −1.75707 | −0.736428 | 1.08730 | 1.40549 | 1.29396 | 1.00000 | 1.60368 | −2.45767 | −2.46955 | ||||||||||||||||||
1.17 | −1.74890 | −3.08410 | 1.05865 | −3.45153 | 5.39379 | 1.00000 | 1.64633 | 6.51170 | 6.03637 | ||||||||||||||||||
1.18 | −1.65910 | 2.86279 | 0.752617 | −1.19236 | −4.74966 | 1.00000 | 2.06953 | 5.19558 | 1.97825 | ||||||||||||||||||
1.19 | −1.63801 | 0.0795943 | 0.683081 | 2.69489 | −0.130376 | 1.00000 | 2.15713 | −2.99366 | −4.41426 | ||||||||||||||||||
1.20 | −1.50497 | −2.68721 | 0.264943 | −2.50384 | 4.04418 | 1.00000 | 2.61121 | 4.22109 | 3.76821 | ||||||||||||||||||
See all 64 embeddings |
Atkin-Lehner signs
\( p \) | Sign |
---|---|
\(7\) | \(-1\) |
\(31\) | \(1\) |
\(37\) | \(-1\) |
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 | 8029.2.a.b | ✓ | 64 |
By twisted newform orbit | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Mult | Type |
8029.2.a.b | ✓ | 64 | 1.a | even | 1 | 1 | trivial |