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: | \(43\) |
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 | −3.34431 | 1.00000 | −3.91124 | 3.34431 | 0.821669 | −1.00000 | 8.18441 | 3.91124 | ||||||||||||||||||
1.2 | −1.00000 | −3.24783 | 1.00000 | 2.20422 | 3.24783 | 3.82287 | −1.00000 | 7.54837 | −2.20422 | ||||||||||||||||||
1.3 | −1.00000 | −2.91293 | 1.00000 | 2.71400 | 2.91293 | 1.04550 | −1.00000 | 5.48515 | −2.71400 | ||||||||||||||||||
1.4 | −1.00000 | −2.88859 | 1.00000 | −0.162345 | 2.88859 | −3.68356 | −1.00000 | 5.34393 | 0.162345 | ||||||||||||||||||
1.5 | −1.00000 | −2.71486 | 1.00000 | −0.740916 | 2.71486 | 4.34624 | −1.00000 | 4.37046 | 0.740916 | ||||||||||||||||||
1.6 | −1.00000 | −2.54429 | 1.00000 | −4.40933 | 2.54429 | −2.39004 | −1.00000 | 3.47339 | 4.40933 | ||||||||||||||||||
1.7 | −1.00000 | −2.53282 | 1.00000 | 2.86896 | 2.53282 | 3.12244 | −1.00000 | 3.41520 | −2.86896 | ||||||||||||||||||
1.8 | −1.00000 | −2.22097 | 1.00000 | 0.529365 | 2.22097 | −2.58907 | −1.00000 | 1.93269 | −0.529365 | ||||||||||||||||||
1.9 | −1.00000 | −2.12309 | 1.00000 | 0.333090 | 2.12309 | −1.76432 | −1.00000 | 1.50753 | −0.333090 | ||||||||||||||||||
1.10 | −1.00000 | −2.06580 | 1.00000 | 4.42069 | 2.06580 | −2.80943 | −1.00000 | 1.26754 | −4.42069 | ||||||||||||||||||
1.11 | −1.00000 | −1.98111 | 1.00000 | −2.70035 | 1.98111 | 2.97081 | −1.00000 | 0.924794 | 2.70035 | ||||||||||||||||||
1.12 | −1.00000 | −1.78337 | 1.00000 | −3.15111 | 1.78337 | −2.13059 | −1.00000 | 0.180410 | 3.15111 | ||||||||||||||||||
1.13 | −1.00000 | −1.49345 | 1.00000 | 1.29948 | 1.49345 | −1.68221 | −1.00000 | −0.769617 | −1.29948 | ||||||||||||||||||
1.14 | −1.00000 | −1.36513 | 1.00000 | 0.286730 | 1.36513 | −1.35155 | −1.00000 | −1.13641 | −0.286730 | ||||||||||||||||||
1.15 | −1.00000 | −1.12203 | 1.00000 | −3.99522 | 1.12203 | 0.851275 | −1.00000 | −1.74104 | 3.99522 | ||||||||||||||||||
1.16 | −1.00000 | −1.11378 | 1.00000 | 4.02830 | 1.11378 | 1.02145 | −1.00000 | −1.75949 | −4.02830 | ||||||||||||||||||
1.17 | −1.00000 | −1.00471 | 1.00000 | −1.06211 | 1.00471 | 0.645369 | −1.00000 | −1.99055 | 1.06211 | ||||||||||||||||||
1.18 | −1.00000 | −0.978925 | 1.00000 | −2.13476 | 0.978925 | 5.08930 | −1.00000 | −2.04171 | 2.13476 | ||||||||||||||||||
1.19 | −1.00000 | −0.765202 | 1.00000 | −1.80247 | 0.765202 | 4.51708 | −1.00000 | −2.41447 | 1.80247 | ||||||||||||||||||
1.20 | −1.00000 | −0.649534 | 1.00000 | 3.59840 | 0.649534 | 4.54706 | −1.00000 | −2.57811 | −3.59840 | ||||||||||||||||||
See all 43 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.i | ✓ | 43 |
By twisted newform orbit | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Mult | Type |
8018.2.a.i | ✓ | 43 | 1.a | even | 1 | 1 | trivial |
Hecke kernels
This newform subspace can be constructed as the kernel of the linear operator \( T_{3}^{43} - 91 T_{3}^{41} - 5 T_{3}^{40} + 3817 T_{3}^{39} + 412 T_{3}^{38} - 97975 T_{3}^{37} + \cdots + 19296472 \) acting on \(S_{2}^{\mathrm{new}}(\Gamma_0(8018))\).