Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [8019,2,Mod(1,8019)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(8019, 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("8019.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 8019 = 3^{6} \cdot 11 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 8019.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: | \(64.0320373809\) |
Analytic rank: | \(0\) |
Dimension: | \(21\) |
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 | −2.36924 | 0 | 3.61332 | 0.785442 | 0 | 1.53278 | −3.82234 | 0 | −1.86090 | ||||||||||||||||||
1.2 | −2.25922 | 0 | 3.10409 | −1.06996 | 0 | −0.137444 | −2.49438 | 0 | 2.41727 | ||||||||||||||||||
1.3 | −2.07274 | 0 | 2.29625 | 0.494134 | 0 | −1.40906 | −0.614038 | 0 | −1.02421 | ||||||||||||||||||
1.4 | −1.44357 | 0 | 0.0839057 | 3.26538 | 0 | −0.792935 | 2.76602 | 0 | −4.71382 | ||||||||||||||||||
1.5 | −1.33160 | 0 | −0.226829 | −3.20854 | 0 | −2.77782 | 2.96526 | 0 | 4.27251 | ||||||||||||||||||
1.6 | −1.29986 | 0 | −0.310353 | −2.12386 | 0 | −3.41757 | 3.00315 | 0 | 2.76073 | ||||||||||||||||||
1.7 | −1.01172 | 0 | −0.976420 | 4.44905 | 0 | 2.99336 | 3.01131 | 0 | −4.50120 | ||||||||||||||||||
1.8 | −0.521281 | 0 | −1.72827 | 0.302159 | 0 | 0.215327 | 1.94347 | 0 | −0.157510 | ||||||||||||||||||
1.9 | −0.455991 | 0 | −1.79207 | −3.13439 | 0 | 0.856728 | 1.72915 | 0 | 1.42925 | ||||||||||||||||||
1.10 | −0.0682043 | 0 | −1.99535 | 1.18434 | 0 | −4.66035 | 0.272500 | 0 | −0.0807768 | ||||||||||||||||||
1.11 | 0.563863 | 0 | −1.68206 | 4.27233 | 0 | 0.945321 | −2.07618 | 0 | 2.40901 | ||||||||||||||||||
1.12 | 0.878744 | 0 | −1.22781 | 1.62071 | 0 | 2.93534 | −2.83642 | 0 | 1.42419 | ||||||||||||||||||
1.13 | 1.02284 | 0 | −0.953805 | 2.76466 | 0 | −3.04869 | −3.02126 | 0 | 2.82779 | ||||||||||||||||||
1.14 | 1.38639 | 0 | −0.0779333 | −2.26790 | 0 | −0.965210 | −2.88082 | 0 | −3.14419 | ||||||||||||||||||
1.15 | 1.40249 | 0 | −0.0330274 | −1.97794 | 0 | 1.49830 | −2.85130 | 0 | −2.77404 | ||||||||||||||||||
1.16 | 1.57842 | 0 | 0.491400 | 2.27349 | 0 | 2.42031 | −2.38120 | 0 | 3.58851 | ||||||||||||||||||
1.17 | 1.73645 | 0 | 1.01527 | −0.0241179 | 0 | −4.08219 | −1.70994 | 0 | −0.0418795 | ||||||||||||||||||
1.18 | 2.38894 | 0 | 3.70703 | −1.18459 | 0 | −1.03676 | 4.07800 | 0 | −2.82991 | ||||||||||||||||||
1.19 | 2.51933 | 0 | 4.34701 | 0.0919030 | 0 | 4.54767 | 5.91287 | 0 | 0.231534 | ||||||||||||||||||
1.20 | 2.64385 | 0 | 4.98995 | 1.69587 | 0 | 0.416922 | 7.90499 | 0 | 4.48364 | ||||||||||||||||||
See all 21 embeddings |
Atkin-Lehner signs
\( p \) | Sign |
---|---|
\(3\) | \(-1\) |
\(11\) | \(1\) |
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 | 8019.2.a.f | yes | 21 |
3.b | odd | 2 | 1 | 8019.2.a.c | ✓ | 21 |
By twisted newform orbit | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Mult | Type |
8019.2.a.c | ✓ | 21 | 3.b | odd | 2 | 1 | |
8019.2.a.f | yes | 21 | 1.a | even | 1 | 1 | trivial |
Hecke kernels
This newform subspace can be constructed as the kernel of the linear operator \( T_{2}^{21} - 6 T_{2}^{20} - 12 T_{2}^{19} + 130 T_{2}^{18} - 24 T_{2}^{17} - 1146 T_{2}^{16} + 1083 T_{2}^{15} + \cdots - 53 \) acting on \(S_{2}^{\mathrm{new}}(\Gamma_0(8019))\).