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: | \(41\) |
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 | −3.10704 | 1.00000 | −3.25849 | 3.10704 | 4.58720 | −1.00000 | 6.65369 | 3.25849 | ||||||||||||||||||
1.2 | −1.00000 | −2.99911 | 1.00000 | 0.291646 | 2.99911 | −2.03701 | −1.00000 | 5.99467 | −0.291646 | ||||||||||||||||||
1.3 | −1.00000 | −2.94121 | 1.00000 | −2.18985 | 2.94121 | −0.696753 | −1.00000 | 5.65074 | 2.18985 | ||||||||||||||||||
1.4 | −1.00000 | −2.61753 | 1.00000 | 0.199936 | 2.61753 | 0.481093 | −1.00000 | 3.85148 | −0.199936 | ||||||||||||||||||
1.5 | −1.00000 | −2.52494 | 1.00000 | 2.43918 | 2.52494 | 0.521147 | −1.00000 | 3.37531 | −2.43918 | ||||||||||||||||||
1.6 | −1.00000 | −2.15334 | 1.00000 | −3.70592 | 2.15334 | −3.79982 | −1.00000 | 1.63688 | 3.70592 | ||||||||||||||||||
1.7 | −1.00000 | −2.09909 | 1.00000 | 1.36520 | 2.09909 | 4.01442 | −1.00000 | 1.40618 | −1.36520 | ||||||||||||||||||
1.8 | −1.00000 | −1.96501 | 1.00000 | −1.27031 | 1.96501 | 1.60889 | −1.00000 | 0.861269 | 1.27031 | ||||||||||||||||||
1.9 | −1.00000 | −1.82110 | 1.00000 | −3.54712 | 1.82110 | −2.30184 | −1.00000 | 0.316404 | 3.54712 | ||||||||||||||||||
1.10 | −1.00000 | −1.75523 | 1.00000 | −0.0353436 | 1.75523 | −4.74271 | −1.00000 | 0.0808489 | 0.0353436 | ||||||||||||||||||
1.11 | −1.00000 | −1.66216 | 1.00000 | −4.08852 | 1.66216 | 3.79799 | −1.00000 | −0.237209 | 4.08852 | ||||||||||||||||||
1.12 | −1.00000 | −1.48981 | 1.00000 | 2.56048 | 1.48981 | 1.18596 | −1.00000 | −0.780452 | −2.56048 | ||||||||||||||||||
1.13 | −1.00000 | −1.39030 | 1.00000 | 4.04446 | 1.39030 | −1.52895 | −1.00000 | −1.06708 | −4.04446 | ||||||||||||||||||
1.14 | −1.00000 | −1.20998 | 1.00000 | 0.0448427 | 1.20998 | −2.73874 | −1.00000 | −1.53595 | −0.0448427 | ||||||||||||||||||
1.15 | −1.00000 | −0.949118 | 1.00000 | −3.26613 | 0.949118 | 3.22650 | −1.00000 | −2.09917 | 3.26613 | ||||||||||||||||||
1.16 | −1.00000 | −0.776259 | 1.00000 | 2.71672 | 0.776259 | 2.01306 | −1.00000 | −2.39742 | −2.71672 | ||||||||||||||||||
1.17 | −1.00000 | −0.438243 | 1.00000 | −0.442957 | 0.438243 | 2.11643 | −1.00000 | −2.80794 | 0.442957 | ||||||||||||||||||
1.18 | −1.00000 | 0.0343445 | 1.00000 | −1.14164 | −0.0343445 | −1.82320 | −1.00000 | −2.99882 | 1.14164 | ||||||||||||||||||
1.19 | −1.00000 | 0.100035 | 1.00000 | −0.345424 | −0.100035 | 2.97223 | −1.00000 | −2.98999 | 0.345424 | ||||||||||||||||||
1.20 | −1.00000 | 0.237080 | 1.00000 | 0.796437 | −0.237080 | 2.80350 | −1.00000 | −2.94379 | −0.796437 | ||||||||||||||||||
See all 41 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.h | ✓ | 41 |
By twisted newform orbit | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Mult | Type |
8018.2.a.h | ✓ | 41 | 1.a | even | 1 | 1 | trivial |
Hecke kernels
This newform subspace can be constructed as the kernel of the linear operator \( T_{3}^{41} - 8 T_{3}^{40} - 51 T_{3}^{39} + 547 T_{3}^{38} + 913 T_{3}^{37} - 16962 T_{3}^{36} + \cdots + 65735 \) acting on \(S_{2}^{\mathrm{new}}(\Gamma_0(8018))\).