Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [8024,2,Mod(1,8024)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(8024, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 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("8024.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 8024 = 2^{3} \cdot 17 \cdot 59 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 8024.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: | \(64.0719625819\) |
Analytic rank: | \(1\) |
Dimension: | \(22\) |
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 | 0 | −3.05613 | 0 | −1.88060 | 0 | −1.70270 | 0 | 6.33993 | 0 | ||||||||||||||||||
1.2 | 0 | −2.56466 | 0 | −3.26922 | 0 | 2.64610 | 0 | 3.57750 | 0 | ||||||||||||||||||
1.3 | 0 | −2.54005 | 0 | 2.36838 | 0 | 1.43029 | 0 | 3.45187 | 0 | ||||||||||||||||||
1.4 | 0 | −2.48825 | 0 | −0.882528 | 0 | 0.896015 | 0 | 3.19137 | 0 | ||||||||||||||||||
1.5 | 0 | −2.46281 | 0 | 3.32357 | 0 | 0.836555 | 0 | 3.06541 | 0 | ||||||||||||||||||
1.6 | 0 | −2.02290 | 0 | 1.12353 | 0 | −1.44909 | 0 | 1.09211 | 0 | ||||||||||||||||||
1.7 | 0 | −1.63019 | 0 | 0.886839 | 0 | −4.44237 | 0 | −0.342474 | 0 | ||||||||||||||||||
1.8 | 0 | −1.20210 | 0 | 1.10558 | 0 | 3.71217 | 0 | −1.55495 | 0 | ||||||||||||||||||
1.9 | 0 | −0.687639 | 0 | −1.07935 | 0 | 2.48918 | 0 | −2.52715 | 0 | ||||||||||||||||||
1.10 | 0 | −0.484590 | 0 | 2.40120 | 0 | −0.883019 | 0 | −2.76517 | 0 | ||||||||||||||||||
1.11 | 0 | −0.0474813 | 0 | 2.55871 | 0 | −1.15477 | 0 | −2.99775 | 0 | ||||||||||||||||||
1.12 | 0 | 0.159171 | 0 | −4.24792 | 0 | −1.24523 | 0 | −2.97466 | 0 | ||||||||||||||||||
1.13 | 0 | 0.283630 | 0 | −1.81468 | 0 | −4.62526 | 0 | −2.91955 | 0 | ||||||||||||||||||
1.14 | 0 | 0.325143 | 0 | −1.77729 | 0 | 4.59153 | 0 | −2.89428 | 0 | ||||||||||||||||||
1.15 | 0 | 0.535004 | 0 | 2.05543 | 0 | 0.811137 | 0 | −2.71377 | 0 | ||||||||||||||||||
1.16 | 0 | 1.27679 | 0 | 2.13098 | 0 | 3.12134 | 0 | −1.36980 | 0 | ||||||||||||||||||
1.17 | 0 | 1.39463 | 0 | 4.34845 | 0 | −1.84282 | 0 | −1.05500 | 0 | ||||||||||||||||||
1.18 | 0 | 1.49900 | 0 | −0.909441 | 0 | 1.38706 | 0 | −0.753011 | 0 | ||||||||||||||||||
1.19 | 0 | 2.29019 | 0 | 0.921405 | 0 | −4.02395 | 0 | 2.24495 | 0 | ||||||||||||||||||
1.20 | 0 | 2.44950 | 0 | −0.409784 | 0 | −2.49662 | 0 | 3.00004 | 0 | ||||||||||||||||||
See all 22 embeddings |
Atkin-Lehner signs
\( p \) | Sign |
---|---|
\(2\) | \(-1\) |
\(17\) | \(1\) |
\(59\) | \(-1\) |
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 | 8024.2.a.x | ✓ | 22 |
By twisted newform orbit | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Mult | Type |
8024.2.a.x | ✓ | 22 | 1.a | even | 1 | 1 | trivial |
Hecke kernels
This newform subspace can be constructed as the intersection of the kernels of the following linear operators acting on \(S_{2}^{\mathrm{new}}(\Gamma_0(8024))\):
\( T_{3}^{22} + 3 T_{3}^{21} - 35 T_{3}^{20} - 108 T_{3}^{19} + 496 T_{3}^{18} + 1583 T_{3}^{17} - 3686 T_{3}^{16} + \cdots - 8 \) |
\( T_{5}^{22} - 3 T_{5}^{21} - 52 T_{5}^{20} + 158 T_{5}^{19} + 1065 T_{5}^{18} - 3304 T_{5}^{17} + \cdots - 70610 \) |
\( T_{7}^{22} - 74 T_{7}^{20} + 15 T_{7}^{19} + 2222 T_{7}^{18} - 790 T_{7}^{17} - 35244 T_{7}^{16} + \cdots - 1177210 \) |