Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [6026,2,Mod(1,6026)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(6026, 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("6026.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 6026 = 2 \cdot 23 \cdot 131 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 6026.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: | \(48.1178522580\) |
Analytic rank: | \(1\) |
Dimension: | \(21\) |
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 | −3.25554 | 1.00000 | 0.398003 | −3.25554 | 0.686920 | 1.00000 | 7.59851 | 0.398003 | ||||||||||||||||||
1.2 | 1.00000 | −2.96739 | 1.00000 | −0.775054 | −2.96739 | 0.413858 | 1.00000 | 5.80542 | −0.775054 | ||||||||||||||||||
1.3 | 1.00000 | −2.37676 | 1.00000 | −2.07688 | −2.37676 | −0.108208 | 1.00000 | 2.64897 | −2.07688 | ||||||||||||||||||
1.4 | 1.00000 | −1.87480 | 1.00000 | 0.417125 | −1.87480 | −3.88487 | 1.00000 | 0.514862 | 0.417125 | ||||||||||||||||||
1.5 | 1.00000 | −1.74967 | 1.00000 | 2.79997 | −1.74967 | 0.229508 | 1.00000 | 0.0613311 | 2.79997 | ||||||||||||||||||
1.6 | 1.00000 | −1.31043 | 1.00000 | −3.45176 | −1.31043 | −4.90131 | 1.00000 | −1.28277 | −3.45176 | ||||||||||||||||||
1.7 | 1.00000 | −1.30046 | 1.00000 | −2.98653 | −1.30046 | 2.26537 | 1.00000 | −1.30880 | −2.98653 | ||||||||||||||||||
1.8 | 1.00000 | −1.08114 | 1.00000 | 0.379081 | −1.08114 | 0.614832 | 1.00000 | −1.83113 | 0.379081 | ||||||||||||||||||
1.9 | 1.00000 | −0.293262 | 1.00000 | 2.91518 | −0.293262 | −1.20061 | 1.00000 | −2.91400 | 2.91518 | ||||||||||||||||||
1.10 | 1.00000 | −0.104929 | 1.00000 | −0.922657 | −0.104929 | 4.49446 | 1.00000 | −2.98899 | −0.922657 | ||||||||||||||||||
1.11 | 1.00000 | 0.104111 | 1.00000 | 1.37645 | 0.104111 | −2.65513 | 1.00000 | −2.98916 | 1.37645 | ||||||||||||||||||
1.12 | 1.00000 | 0.775060 | 1.00000 | 0.913280 | 0.775060 | −1.54834 | 1.00000 | −2.39928 | 0.913280 | ||||||||||||||||||
1.13 | 1.00000 | 0.780842 | 1.00000 | −0.582778 | 0.780842 | 2.23605 | 1.00000 | −2.39029 | −0.582778 | ||||||||||||||||||
1.14 | 1.00000 | 0.825726 | 1.00000 | −2.91252 | 0.825726 | −1.72528 | 1.00000 | −2.31818 | −2.91252 | ||||||||||||||||||
1.15 | 1.00000 | 0.938474 | 1.00000 | 0.929839 | 0.938474 | −1.00873 | 1.00000 | −2.11927 | 0.929839 | ||||||||||||||||||
1.16 | 1.00000 | 1.13204 | 1.00000 | −3.67213 | 1.13204 | −0.943976 | 1.00000 | −1.71848 | −3.67213 | ||||||||||||||||||
1.17 | 1.00000 | 1.44805 | 1.00000 | 3.26245 | 1.44805 | −3.72778 | 1.00000 | −0.903151 | 3.26245 | ||||||||||||||||||
1.18 | 1.00000 | 1.90172 | 1.00000 | −3.81206 | 1.90172 | 1.69979 | 1.00000 | 0.616557 | −3.81206 | ||||||||||||||||||
1.19 | 1.00000 | 2.43324 | 1.00000 | −0.544807 | 2.43324 | −1.90449 | 1.00000 | 2.92064 | −0.544807 | ||||||||||||||||||
1.20 | 1.00000 | 2.71715 | 1.00000 | −1.49550 | 2.71715 | −4.64653 | 1.00000 | 4.38289 | −1.49550 | ||||||||||||||||||
See all 21 embeddings |
Atkin-Lehner signs
\( p \) | Sign |
---|---|
\(2\) | \(-1\) |
\(23\) | \(1\) |
\(131\) | \(-1\) |
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 | 6026.2.a.g | ✓ | 21 |
By twisted newform orbit | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Mult | Type |
6026.2.a.g | ✓ | 21 | 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 \(S_{2}^{\mathrm{new}}(\Gamma_0(6026))\):
\( T_{3}^{21} - 35 T_{3}^{19} + 3 T_{3}^{18} + 494 T_{3}^{17} - 88 T_{3}^{16} - 3661 T_{3}^{15} + 1012 T_{3}^{14} + 15586 T_{3}^{13} - 5966 T_{3}^{12} - 39200 T_{3}^{11} + 19523 T_{3}^{10} + 57285 T_{3}^{9} - 35664 T_{3}^{8} + \cdots - 14 \) |
\( T_{5}^{21} + 13 T_{5}^{20} + 31 T_{5}^{19} - 277 T_{5}^{18} - 1485 T_{5}^{17} + 679 T_{5}^{16} + 17587 T_{5}^{15} + 21616 T_{5}^{14} - 79704 T_{5}^{13} - 183069 T_{5}^{12} + 107778 T_{5}^{11} + 518881 T_{5}^{10} + \cdots - 1834 \) |