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: | \(0\) |
Dimension: | \(49\) |
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 | −3.18331 | 1.00000 | 4.19262 | −3.18331 | −3.25533 | 1.00000 | 7.13346 | 4.19262 | ||||||||||||||||||
1.2 | 1.00000 | −3.16496 | 1.00000 | −1.03983 | −3.16496 | −1.27872 | 1.00000 | 7.01700 | −1.03983 | ||||||||||||||||||
1.3 | 1.00000 | −3.03631 | 1.00000 | −0.470191 | −3.03631 | 3.61227 | 1.00000 | 6.21915 | −0.470191 | ||||||||||||||||||
1.4 | 1.00000 | −3.03421 | 1.00000 | −2.36281 | −3.03421 | −0.910676 | 1.00000 | 6.20641 | −2.36281 | ||||||||||||||||||
1.5 | 1.00000 | −2.78216 | 1.00000 | 3.32795 | −2.78216 | 4.62132 | 1.00000 | 4.74040 | 3.32795 | ||||||||||||||||||
1.6 | 1.00000 | −2.76297 | 1.00000 | 0.238506 | −2.76297 | 2.08661 | 1.00000 | 4.63399 | 0.238506 | ||||||||||||||||||
1.7 | 1.00000 | −2.47584 | 1.00000 | 1.97954 | −2.47584 | −2.02339 | 1.00000 | 3.12981 | 1.97954 | ||||||||||||||||||
1.8 | 1.00000 | −2.35762 | 1.00000 | −3.55313 | −2.35762 | −1.02341 | 1.00000 | 2.55835 | −3.55313 | ||||||||||||||||||
1.9 | 1.00000 | −2.16417 | 1.00000 | 3.75376 | −2.16417 | 4.09027 | 1.00000 | 1.68362 | 3.75376 | ||||||||||||||||||
1.10 | 1.00000 | −2.15958 | 1.00000 | −0.594727 | −2.15958 | 4.60099 | 1.00000 | 1.66376 | −0.594727 | ||||||||||||||||||
1.11 | 1.00000 | −1.57817 | 1.00000 | −2.42122 | −1.57817 | −1.17267 | 1.00000 | −0.509368 | −2.42122 | ||||||||||||||||||
1.12 | 1.00000 | −1.45260 | 1.00000 | 2.56447 | −1.45260 | −3.76816 | 1.00000 | −0.889956 | 2.56447 | ||||||||||||||||||
1.13 | 1.00000 | −1.41679 | 1.00000 | −3.74277 | −1.41679 | 3.98944 | 1.00000 | −0.992702 | −3.74277 | ||||||||||||||||||
1.14 | 1.00000 | −1.33535 | 1.00000 | 0.425182 | −1.33535 | −2.10915 | 1.00000 | −1.21683 | 0.425182 | ||||||||||||||||||
1.15 | 1.00000 | −1.22925 | 1.00000 | −2.52525 | −1.22925 | 3.13859 | 1.00000 | −1.48895 | −2.52525 | ||||||||||||||||||
1.16 | 1.00000 | −1.06684 | 1.00000 | 3.41038 | −1.06684 | −0.896941 | 1.00000 | −1.86186 | 3.41038 | ||||||||||||||||||
1.17 | 1.00000 | −0.823102 | 1.00000 | 1.30158 | −0.823102 | 0.990463 | 1.00000 | −2.32250 | 1.30158 | ||||||||||||||||||
1.18 | 1.00000 | −0.655875 | 1.00000 | 3.82378 | −0.655875 | −1.10690 | 1.00000 | −2.56983 | 3.82378 | ||||||||||||||||||
1.19 | 1.00000 | −0.460040 | 1.00000 | −0.746209 | −0.460040 | −4.50236 | 1.00000 | −2.78836 | −0.746209 | ||||||||||||||||||
1.20 | 1.00000 | −0.411559 | 1.00000 | −1.49400 | −0.411559 | −1.21130 | 1.00000 | −2.83062 | −1.49400 | ||||||||||||||||||
See all 49 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.k | ✓ | 49 |
By twisted newform orbit | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Mult | Type |
8018.2.a.k | ✓ | 49 | 1.a | even | 1 | 1 | trivial |
Hecke kernels
This newform subspace can be constructed as the kernel of the linear operator \( T_{3}^{49} - 13 T_{3}^{48} - 22 T_{3}^{47} + 982 T_{3}^{46} - 2059 T_{3}^{45} - 32106 T_{3}^{44} + \cdots + 838784 \) acting on \(S_{2}^{\mathrm{new}}(\Gamma_0(8018))\).