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: | \(47\) |
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 | −3.22214 | 1.00000 | 3.63661 | −3.22214 | −0.166372 | 1.00000 | 7.38220 | 3.63661 | ||||||||||||||||||
1.2 | 1.00000 | −3.13813 | 1.00000 | 2.17673 | −3.13813 | 2.94096 | 1.00000 | 6.84787 | 2.17673 | ||||||||||||||||||
1.3 | 1.00000 | −3.07943 | 1.00000 | −3.30634 | −3.07943 | −2.62160 | 1.00000 | 6.48290 | −3.30634 | ||||||||||||||||||
1.4 | 1.00000 | −2.90959 | 1.00000 | −4.15278 | −2.90959 | 3.02073 | 1.00000 | 5.46571 | −4.15278 | ||||||||||||||||||
1.5 | 1.00000 | −2.83191 | 1.00000 | 1.28371 | −2.83191 | −4.11947 | 1.00000 | 5.01973 | 1.28371 | ||||||||||||||||||
1.6 | 1.00000 | −2.78985 | 1.00000 | −2.51493 | −2.78985 | −0.381461 | 1.00000 | 4.78329 | −2.51493 | ||||||||||||||||||
1.7 | 1.00000 | −2.41559 | 1.00000 | 0.828405 | −2.41559 | 0.635145 | 1.00000 | 2.83509 | 0.828405 | ||||||||||||||||||
1.8 | 1.00000 | −2.28341 | 1.00000 | 4.33431 | −2.28341 | −0.955796 | 1.00000 | 2.21398 | 4.33431 | ||||||||||||||||||
1.9 | 1.00000 | −2.19254 | 1.00000 | 1.33631 | −2.19254 | −4.99100 | 1.00000 | 1.80723 | 1.33631 | ||||||||||||||||||
1.10 | 1.00000 | −2.00763 | 1.00000 | −1.79399 | −2.00763 | −2.43862 | 1.00000 | 1.03060 | −1.79399 | ||||||||||||||||||
1.11 | 1.00000 | −1.99735 | 1.00000 | −0.291796 | −1.99735 | −0.492820 | 1.00000 | 0.989407 | −0.291796 | ||||||||||||||||||
1.12 | 1.00000 | −1.51480 | 1.00000 | −1.33044 | −1.51480 | −3.41282 | 1.00000 | −0.705394 | −1.33044 | ||||||||||||||||||
1.13 | 1.00000 | −1.46195 | 1.00000 | 2.14418 | −1.46195 | 2.84565 | 1.00000 | −0.862709 | 2.14418 | ||||||||||||||||||
1.14 | 1.00000 | −1.39823 | 1.00000 | 0.539425 | −1.39823 | 5.05784 | 1.00000 | −1.04494 | 0.539425 | ||||||||||||||||||
1.15 | 1.00000 | −1.14813 | 1.00000 | 2.89240 | −1.14813 | 3.60462 | 1.00000 | −1.68179 | 2.89240 | ||||||||||||||||||
1.16 | 1.00000 | −1.10999 | 1.00000 | 3.90024 | −1.10999 | −4.77719 | 1.00000 | −1.76791 | 3.90024 | ||||||||||||||||||
1.17 | 1.00000 | −1.03614 | 1.00000 | 0.118794 | −1.03614 | 2.13406 | 1.00000 | −1.92642 | 0.118794 | ||||||||||||||||||
1.18 | 1.00000 | −0.833135 | 1.00000 | −3.18557 | −0.833135 | 0.455061 | 1.00000 | −2.30589 | −3.18557 | ||||||||||||||||||
1.19 | 1.00000 | −0.764189 | 1.00000 | −0.445775 | −0.764189 | −0.938446 | 1.00000 | −2.41602 | −0.445775 | ||||||||||||||||||
1.20 | 1.00000 | −0.316697 | 1.00000 | −0.633871 | −0.316697 | 1.30218 | 1.00000 | −2.89970 | −0.633871 | ||||||||||||||||||
See all 47 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.j | ✓ | 47 |
By twisted newform orbit | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Mult | Type |
8018.2.a.j | ✓ | 47 | 1.a | even | 1 | 1 | trivial |
Hecke kernels
This newform subspace can be constructed as the kernel of the linear operator \( T_{3}^{47} - 10 T_{3}^{46} - 55 T_{3}^{45} + 849 T_{3}^{44} + 625 T_{3}^{43} - 32814 T_{3}^{42} + \cdots - 2063488 \) acting on \(S_{2}^{\mathrm{new}}(\Gamma_0(8018))\).