Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [8024,2,Mod(1,8024)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(8024, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 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("8024.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 8024 = 2^{3} \cdot 17 \cdot 59 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 8024.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: | \(64.0719625819\) |
Analytic rank: | \(1\) |
Dimension: | \(23\) |
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 | 0 | −3.24951 | 0 | −3.27317 | 0 | 3.90567 | 0 | 7.55931 | 0 | ||||||||||||||||||
1.2 | 0 | −3.11439 | 0 | 4.12614 | 0 | 1.17263 | 0 | 6.69943 | 0 | ||||||||||||||||||
1.3 | 0 | −2.88993 | 0 | −1.71727 | 0 | −4.47538 | 0 | 5.35170 | 0 | ||||||||||||||||||
1.4 | 0 | −2.64010 | 0 | 3.09841 | 0 | −1.88185 | 0 | 3.97013 | 0 | ||||||||||||||||||
1.5 | 0 | −2.07300 | 0 | −3.30236 | 0 | 0.766448 | 0 | 1.29731 | 0 | ||||||||||||||||||
1.6 | 0 | −1.74430 | 0 | 1.05481 | 0 | 1.84260 | 0 | 0.0425790 | 0 | ||||||||||||||||||
1.7 | 0 | −1.61430 | 0 | −1.23431 | 0 | 4.85046 | 0 | −0.394052 | 0 | ||||||||||||||||||
1.8 | 0 | −1.49807 | 0 | −3.21279 | 0 | −1.95127 | 0 | −0.755772 | 0 | ||||||||||||||||||
1.9 | 0 | −1.40425 | 0 | 3.37446 | 0 | −3.92495 | 0 | −1.02809 | 0 | ||||||||||||||||||
1.10 | 0 | −1.29710 | 0 | −1.23439 | 0 | −2.46133 | 0 | −1.31752 | 0 | ||||||||||||||||||
1.11 | 0 | −0.823534 | 0 | 3.63980 | 0 | 3.42292 | 0 | −2.32179 | 0 | ||||||||||||||||||
1.12 | 0 | −0.725294 | 0 | −2.56147 | 0 | −0.934698 | 0 | −2.47395 | 0 | ||||||||||||||||||
1.13 | 0 | −0.587444 | 0 | 0.0220313 | 0 | 3.20930 | 0 | −2.65491 | 0 | ||||||||||||||||||
1.14 | 0 | 0.453475 | 0 | 2.43721 | 0 | 1.57711 | 0 | −2.79436 | 0 | ||||||||||||||||||
1.15 | 0 | 0.561991 | 0 | −2.34032 | 0 | −3.24647 | 0 | −2.68417 | 0 | ||||||||||||||||||
1.16 | 0 | 1.04245 | 0 | −0.295436 | 0 | 1.92039 | 0 | −1.91330 | 0 | ||||||||||||||||||
1.17 | 0 | 1.25653 | 0 | 3.93457 | 0 | −3.56420 | 0 | −1.42113 | 0 | ||||||||||||||||||
1.18 | 0 | 1.45598 | 0 | −0.727716 | 0 | 2.11595 | 0 | −0.880108 | 0 | ||||||||||||||||||
1.19 | 0 | 2.15021 | 0 | 1.53922 | 0 | −0.745521 | 0 | 1.62340 | 0 | ||||||||||||||||||
1.20 | 0 | 2.41453 | 0 | 0.0537401 | 0 | 0.349134 | 0 | 2.82994 | 0 | ||||||||||||||||||
See all 23 embeddings |
Atkin-Lehner signs
\( p \) | Sign |
---|---|
\(2\) | \(1\) |
\(17\) | \(1\) |
\(59\) | \(1\) |
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 | 8024.2.a.y | ✓ | 23 |
By twisted newform orbit | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Mult | Type |
8024.2.a.y | ✓ | 23 | 1.a | even | 1 | 1 | trivial |
Hecke kernels
This newform subspace can be constructed as the intersection of the kernels of the following linear operators acting on \(S_{2}^{\mathrm{new}}(\Gamma_0(8024))\):
\( T_{3}^{23} + 6 T_{3}^{22} - 28 T_{3}^{21} - 227 T_{3}^{20} + 207 T_{3}^{19} + 3543 T_{3}^{18} + \cdots + 23040 \) |
\( T_{5}^{23} - 73 T_{5}^{21} - 28 T_{5}^{20} + 2274 T_{5}^{19} + 1681 T_{5}^{18} - 39169 T_{5}^{17} + \cdots - 4352 \) |
\( T_{7}^{23} + T_{7}^{22} - 88 T_{7}^{21} - 75 T_{7}^{20} + 3282 T_{7}^{19} + 2207 T_{7}^{18} + \cdots + 16035200 \) |