Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [8026,2,Mod(1,8026)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(8026, 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("8026.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 8026 = 2 \cdot 4013 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 8026.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: | \(64.0879326623\) |
Analytic rank: | \(1\) |
Dimension: | \(71\) |
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 | 1.00000 | −3.33028 | 1.00000 | −2.81719 | −3.33028 | 2.39962 | 1.00000 | 8.09075 | −2.81719 | ||||||||||||||||||
1.2 | 1.00000 | −3.18837 | 1.00000 | 1.76077 | −3.18837 | −1.56118 | 1.00000 | 7.16572 | 1.76077 | ||||||||||||||||||
1.3 | 1.00000 | −3.08324 | 1.00000 | −2.29351 | −3.08324 | −1.56272 | 1.00000 | 6.50635 | −2.29351 | ||||||||||||||||||
1.4 | 1.00000 | −3.00113 | 1.00000 | 2.08729 | −3.00113 | 1.33710 | 1.00000 | 6.00675 | 2.08729 | ||||||||||||||||||
1.5 | 1.00000 | −2.91430 | 1.00000 | −0.167675 | −2.91430 | 0.471775 | 1.00000 | 5.49314 | −0.167675 | ||||||||||||||||||
1.6 | 1.00000 | −2.72893 | 1.00000 | 0.723438 | −2.72893 | −3.46721 | 1.00000 | 4.44707 | 0.723438 | ||||||||||||||||||
1.7 | 1.00000 | −2.59864 | 1.00000 | −3.30872 | −2.59864 | −3.09209 | 1.00000 | 3.75294 | −3.30872 | ||||||||||||||||||
1.8 | 1.00000 | −2.57686 | 1.00000 | −0.429942 | −2.57686 | 3.15501 | 1.00000 | 3.64023 | −0.429942 | ||||||||||||||||||
1.9 | 1.00000 | −2.52707 | 1.00000 | −2.67563 | −2.52707 | −1.45299 | 1.00000 | 3.38607 | −2.67563 | ||||||||||||||||||
1.10 | 1.00000 | −2.46200 | 1.00000 | −1.19890 | −2.46200 | 2.88631 | 1.00000 | 3.06146 | −1.19890 | ||||||||||||||||||
1.11 | 1.00000 | −2.45931 | 1.00000 | 3.45635 | −2.45931 | 3.30103 | 1.00000 | 3.04822 | 3.45635 | ||||||||||||||||||
1.12 | 1.00000 | −2.11692 | 1.00000 | −3.74472 | −2.11692 | 4.88608 | 1.00000 | 1.48134 | −3.74472 | ||||||||||||||||||
1.13 | 1.00000 | −2.05160 | 1.00000 | 2.89935 | −2.05160 | −3.15492 | 1.00000 | 1.20907 | 2.89935 | ||||||||||||||||||
1.14 | 1.00000 | −2.02406 | 1.00000 | 1.61352 | −2.02406 | −3.12008 | 1.00000 | 1.09682 | 1.61352 | ||||||||||||||||||
1.15 | 1.00000 | −2.02372 | 1.00000 | 3.74567 | −2.02372 | 1.02525 | 1.00000 | 1.09543 | 3.74567 | ||||||||||||||||||
1.16 | 1.00000 | −1.97637 | 1.00000 | −0.168031 | −1.97637 | −1.30361 | 1.00000 | 0.906032 | −0.168031 | ||||||||||||||||||
1.17 | 1.00000 | −1.95374 | 1.00000 | 0.792660 | −1.95374 | 2.85182 | 1.00000 | 0.817104 | 0.792660 | ||||||||||||||||||
1.18 | 1.00000 | −1.89918 | 1.00000 | −0.474376 | −1.89918 | 1.52174 | 1.00000 | 0.606869 | −0.474376 | ||||||||||||||||||
1.19 | 1.00000 | −1.72230 | 1.00000 | −4.08988 | −1.72230 | −0.697853 | 1.00000 | −0.0336847 | −4.08988 | ||||||||||||||||||
1.20 | 1.00000 | −1.70684 | 1.00000 | −2.82175 | −1.70684 | 3.08724 | 1.00000 | −0.0867059 | −2.82175 | ||||||||||||||||||
See all 71 embeddings |
Atkin-Lehner signs
\( p \) | Sign |
---|---|
\(2\) | \(-1\) |
\(4013\) | \(-1\) |
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 | 8026.2.a.a | ✓ | 71 |
By twisted newform orbit | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Mult | Type |
8026.2.a.a | ✓ | 71 | 1.a | even | 1 | 1 | trivial |