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: | \(30\) |
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 | −3.23056 | 1.00000 | −3.65226 | −3.23056 | 2.39039 | 1.00000 | 7.43653 | −3.65226 | ||||||||||||||||||
1.2 | 1.00000 | −3.09428 | 1.00000 | 2.68879 | −3.09428 | 2.69798 | 1.00000 | 6.57455 | 2.68879 | ||||||||||||||||||
1.3 | 1.00000 | −2.74076 | 1.00000 | 0.116951 | −2.74076 | −0.997196 | 1.00000 | 4.51179 | 0.116951 | ||||||||||||||||||
1.4 | 1.00000 | −2.56870 | 1.00000 | −1.11955 | −2.56870 | −1.44974 | 1.00000 | 3.59821 | −1.11955 | ||||||||||||||||||
1.5 | 1.00000 | −2.47683 | 1.00000 | −0.567392 | −2.47683 | −4.82108 | 1.00000 | 3.13468 | −0.567392 | ||||||||||||||||||
1.6 | 1.00000 | −2.43818 | 1.00000 | 3.21483 | −2.43818 | −0.555600 | 1.00000 | 2.94471 | 3.21483 | ||||||||||||||||||
1.7 | 1.00000 | −2.39570 | 1.00000 | −3.46674 | −2.39570 | −3.11450 | 1.00000 | 2.73936 | −3.46674 | ||||||||||||||||||
1.8 | 1.00000 | −2.02842 | 1.00000 | 2.47134 | −2.02842 | 1.41486 | 1.00000 | 1.11447 | 2.47134 | ||||||||||||||||||
1.9 | 1.00000 | −1.51420 | 1.00000 | −2.91196 | −1.51420 | −3.75064 | 1.00000 | −0.707195 | −2.91196 | ||||||||||||||||||
1.10 | 1.00000 | −1.46114 | 1.00000 | 1.82408 | −1.46114 | −2.77663 | 1.00000 | −0.865063 | 1.82408 | ||||||||||||||||||
1.11 | 1.00000 | −1.44219 | 1.00000 | −1.29569 | −1.44219 | 1.46621 | 1.00000 | −0.920075 | −1.29569 | ||||||||||||||||||
1.12 | 1.00000 | −1.14046 | 1.00000 | 1.90163 | −1.14046 | 2.39414 | 1.00000 | −1.69934 | 1.90163 | ||||||||||||||||||
1.13 | 1.00000 | −0.894762 | 1.00000 | −0.0669598 | −0.894762 | 1.42997 | 1.00000 | −2.19940 | −0.0669598 | ||||||||||||||||||
1.14 | 1.00000 | −0.851234 | 1.00000 | −2.73591 | −0.851234 | 0.590237 | 1.00000 | −2.27540 | −2.73591 | ||||||||||||||||||
1.15 | 1.00000 | −0.785531 | 1.00000 | −1.33472 | −0.785531 | 4.52537 | 1.00000 | −2.38294 | −1.33472 | ||||||||||||||||||
1.16 | 1.00000 | −0.219326 | 1.00000 | 2.27443 | −0.219326 | −3.32577 | 1.00000 | −2.95190 | 2.27443 | ||||||||||||||||||
1.17 | 1.00000 | 0.180143 | 1.00000 | 0.229721 | 0.180143 | −1.11361 | 1.00000 | −2.96755 | 0.229721 | ||||||||||||||||||
1.18 | 1.00000 | 0.460726 | 1.00000 | 0.645126 | 0.460726 | 1.69833 | 1.00000 | −2.78773 | 0.645126 | ||||||||||||||||||
1.19 | 1.00000 | 0.677734 | 1.00000 | −4.37664 | 0.677734 | −1.03965 | 1.00000 | −2.54068 | −4.37664 | ||||||||||||||||||
1.20 | 1.00000 | 0.846820 | 1.00000 | 2.51574 | 0.846820 | −3.73115 | 1.00000 | −2.28290 | 2.51574 | ||||||||||||||||||
See all 30 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.d | ✓ | 30 |
By twisted newform orbit | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Mult | Type |
8018.2.a.d | ✓ | 30 | 1.a | even | 1 | 1 | trivial |
Hecke kernels
This newform subspace can be constructed as the kernel of the linear operator \( T_{3}^{30} + 10 T_{3}^{29} - 301 T_{3}^{27} - 658 T_{3}^{26} + 3693 T_{3}^{25} + 12977 T_{3}^{24} + \cdots + 5806 \) acting on \(S_{2}^{\mathrm{new}}(\Gamma_0(8018))\).