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 | −3.32805 | 1.00000 | 2.33043 | 3.32805 | −1.71896 | −1.00000 | 8.07595 | −2.33043 | ||||||||||||||||||
1.2 | −1.00000 | −3.23421 | 1.00000 | −1.01489 | 3.23421 | 2.27890 | −1.00000 | 7.46011 | 1.01489 | ||||||||||||||||||
1.3 | −1.00000 | −3.00067 | 1.00000 | −2.58515 | 3.00067 | −5.14244 | −1.00000 | 6.00401 | 2.58515 | ||||||||||||||||||
1.4 | −1.00000 | −2.69123 | 1.00000 | 2.65985 | 2.69123 | −4.28568 | −1.00000 | 4.24273 | −2.65985 | ||||||||||||||||||
1.5 | −1.00000 | −2.58591 | 1.00000 | −1.96812 | 2.58591 | −0.600261 | −1.00000 | 3.68694 | 1.96812 | ||||||||||||||||||
1.6 | −1.00000 | −2.57203 | 1.00000 | 3.90529 | 2.57203 | −2.74849 | −1.00000 | 3.61534 | −3.90529 | ||||||||||||||||||
1.7 | −1.00000 | −2.37210 | 1.00000 | −2.30761 | 2.37210 | 0.129234 | −1.00000 | 2.62686 | 2.30761 | ||||||||||||||||||
1.8 | −1.00000 | −2.35248 | 1.00000 | 0.260869 | 2.35248 | 1.92119 | −1.00000 | 2.53416 | −0.260869 | ||||||||||||||||||
1.9 | −1.00000 | −1.88003 | 1.00000 | 1.30460 | 1.88003 | −0.890859 | −1.00000 | 0.534497 | −1.30460 | ||||||||||||||||||
1.10 | −1.00000 | −1.50410 | 1.00000 | 0.693241 | 1.50410 | 2.70952 | −1.00000 | −0.737675 | −0.693241 | ||||||||||||||||||
1.11 | −1.00000 | −1.36628 | 1.00000 | 2.24574 | 1.36628 | 3.44497 | −1.00000 | −1.13329 | −2.24574 | ||||||||||||||||||
1.12 | −1.00000 | −1.32663 | 1.00000 | −0.835058 | 1.32663 | −1.21991 | −1.00000 | −1.24006 | 0.835058 | ||||||||||||||||||
1.13 | −1.00000 | −1.30982 | 1.00000 | 1.77709 | 1.30982 | −3.58679 | −1.00000 | −1.28436 | −1.77709 | ||||||||||||||||||
1.14 | −1.00000 | −1.00694 | 1.00000 | −1.74347 | 1.00694 | −4.04026 | −1.00000 | −1.98607 | 1.74347 | ||||||||||||||||||
1.15 | −1.00000 | −0.597156 | 1.00000 | −2.37023 | 0.597156 | 1.41575 | −1.00000 | −2.64341 | 2.37023 | ||||||||||||||||||
1.16 | −1.00000 | −0.562142 | 1.00000 | 1.56640 | 0.562142 | 3.17308 | −1.00000 | −2.68400 | −1.56640 | ||||||||||||||||||
1.17 | −1.00000 | −0.129854 | 1.00000 | 1.90646 | 0.129854 | −0.0260326 | −1.00000 | −2.98314 | −1.90646 | ||||||||||||||||||
1.18 | −1.00000 | 0.0912120 | 1.00000 | −2.07635 | −0.0912120 | −4.23935 | −1.00000 | −2.99168 | 2.07635 | ||||||||||||||||||
1.19 | −1.00000 | 0.129131 | 1.00000 | −3.52572 | −0.129131 | −2.82586 | −1.00000 | −2.98333 | 3.52572 | ||||||||||||||||||
1.20 | −1.00000 | 0.234828 | 1.00000 | −3.98534 | −0.234828 | 1.98646 | −1.00000 | −2.94486 | 3.98534 | ||||||||||||||||||
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.g | ✓ | 34 |
By twisted newform orbit | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Mult | Type |
8018.2.a.g | ✓ | 34 | 1.a | even | 1 | 1 | trivial |
Hecke kernels
This newform subspace can be constructed as the kernel of the linear operator \( T_{3}^{34} + 6 T_{3}^{33} - 48 T_{3}^{32} - 341 T_{3}^{31} + 932 T_{3}^{30} + 8611 T_{3}^{29} + \cdots - 800 \) acting on \(S_{2}^{\mathrm{new}}(\Gamma_0(8018))\).