Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [8018,2,Mod(1,8018)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(8018, 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("8018.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 8018 = 2 \cdot 19 \cdot 211 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 8018.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: | \(64.0240523407\) |
Analytic rank: | \(1\) |
Dimension: | \(34\) |
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 | −3.31570 | 1.00000 | −0.532224 | 3.31570 | −2.51205 | −1.00000 | 7.99387 | 0.532224 | ||||||||||||||||||
1.2 | −1.00000 | −3.17050 | 1.00000 | 4.15425 | 3.17050 | 1.45443 | −1.00000 | 7.05209 | −4.15425 | ||||||||||||||||||
1.3 | −1.00000 | −3.15270 | 1.00000 | −2.25930 | 3.15270 | −1.49908 | −1.00000 | 6.93949 | 2.25930 | ||||||||||||||||||
1.4 | −1.00000 | −3.08799 | 1.00000 | 2.62819 | 3.08799 | −3.66609 | −1.00000 | 6.53566 | −2.62819 | ||||||||||||||||||
1.5 | −1.00000 | −2.56521 | 1.00000 | 3.62382 | 2.56521 | 4.81473 | −1.00000 | 3.58031 | −3.62382 | ||||||||||||||||||
1.6 | −1.00000 | −2.52151 | 1.00000 | −1.30481 | 2.52151 | 0.799571 | −1.00000 | 3.35801 | 1.30481 | ||||||||||||||||||
1.7 | −1.00000 | −2.46365 | 1.00000 | −0.0638040 | 2.46365 | 3.24244 | −1.00000 | 3.06956 | 0.0638040 | ||||||||||||||||||
1.8 | −1.00000 | −2.15742 | 1.00000 | −2.78011 | 2.15742 | −1.33229 | −1.00000 | 1.65446 | 2.78011 | ||||||||||||||||||
1.9 | −1.00000 | −2.09965 | 1.00000 | 1.88296 | 2.09965 | −4.81740 | −1.00000 | 1.40851 | −1.88296 | ||||||||||||||||||
1.10 | −1.00000 | −2.04582 | 1.00000 | −4.09434 | 2.04582 | 1.49846 | −1.00000 | 1.18539 | 4.09434 | ||||||||||||||||||
1.11 | −1.00000 | −1.91986 | 1.00000 | 0.472260 | 1.91986 | 4.62137 | −1.00000 | 0.685870 | −0.472260 | ||||||||||||||||||
1.12 | −1.00000 | −1.71717 | 1.00000 | 1.96614 | 1.71717 | 0.664883 | −1.00000 | −0.0513372 | −1.96614 | ||||||||||||||||||
1.13 | −1.00000 | −1.39250 | 1.00000 | 3.35741 | 1.39250 | −0.849778 | −1.00000 | −1.06096 | −3.35741 | ||||||||||||||||||
1.14 | −1.00000 | −1.11253 | 1.00000 | −2.63739 | 1.11253 | −4.04134 | −1.00000 | −1.76228 | 2.63739 | ||||||||||||||||||
1.15 | −1.00000 | −0.916646 | 1.00000 | −1.80395 | 0.916646 | −2.30047 | −1.00000 | −2.15976 | 1.80395 | ||||||||||||||||||
1.16 | −1.00000 | −0.860547 | 1.00000 | 2.52015 | 0.860547 | −0.0296623 | −1.00000 | −2.25946 | −2.52015 | ||||||||||||||||||
1.17 | −1.00000 | −0.656283 | 1.00000 | −1.22883 | 0.656283 | 2.46640 | −1.00000 | −2.56929 | 1.22883 | ||||||||||||||||||
1.18 | −1.00000 | −0.358038 | 1.00000 | 3.12453 | 0.358038 | −3.38298 | −1.00000 | −2.87181 | −3.12453 | ||||||||||||||||||
1.19 | −1.00000 | −0.350444 | 1.00000 | −0.178230 | 0.350444 | −3.90849 | −1.00000 | −2.87719 | 0.178230 | ||||||||||||||||||
1.20 | −1.00000 | 0.100558 | 1.00000 | 2.02652 | −0.100558 | 1.91249 | −1.00000 | −2.98989 | −2.02652 | ||||||||||||||||||
See all 34 embeddings |
Atkin-Lehner signs
\( p \) | Sign |
---|---|
\(2\) | \(1\) |
\(19\) | \(1\) |
\(211\) | \(1\) |
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 | 8018.2.a.f | ✓ | 34 |
By twisted newform orbit | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Mult | Type |
8018.2.a.f | ✓ | 34 | 1.a | even | 1 | 1 | trivial |
Hecke kernels
This newform subspace can be constructed as the kernel of the linear operator \( T_{3}^{34} + 10 T_{3}^{33} - 20 T_{3}^{32} - 503 T_{3}^{31} - 570 T_{3}^{30} + 10833 T_{3}^{29} + \cdots - 757728 \) acting on \(S_{2}^{\mathrm{new}}(\Gamma_0(8018))\).