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: | \(0\) |
Dimension: | \(33\) |
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 | −3.30495 | 1.00000 | 3.30220 | 3.30495 | 3.90022 | −1.00000 | 7.92270 | −3.30220 | ||||||||||||||||||
1.2 | −1.00000 | −2.92506 | 1.00000 | 0.618794 | 2.92506 | −2.50272 | −1.00000 | 5.55600 | −0.618794 | ||||||||||||||||||
1.3 | −1.00000 | −2.90304 | 1.00000 | −1.99628 | 2.90304 | −0.299170 | −1.00000 | 5.42764 | 1.99628 | ||||||||||||||||||
1.4 | −1.00000 | −2.82338 | 1.00000 | −3.52183 | 2.82338 | 3.82891 | −1.00000 | 4.97150 | 3.52183 | ||||||||||||||||||
1.5 | −1.00000 | −2.71066 | 1.00000 | −2.38566 | 2.71066 | −4.13924 | −1.00000 | 4.34767 | 2.38566 | ||||||||||||||||||
1.6 | −1.00000 | −2.31184 | 1.00000 | −1.83764 | 2.31184 | 0.291912 | −1.00000 | 2.34459 | 1.83764 | ||||||||||||||||||
1.7 | −1.00000 | −1.90551 | 1.00000 | 3.90912 | 1.90551 | 1.35086 | −1.00000 | 0.630974 | −3.90912 | ||||||||||||||||||
1.8 | −1.00000 | −1.82570 | 1.00000 | −3.75704 | 1.82570 | 0.299528 | −1.00000 | 0.333191 | 3.75704 | ||||||||||||||||||
1.9 | −1.00000 | −1.80561 | 1.00000 | −1.32735 | 1.80561 | −4.32567 | −1.00000 | 0.260232 | 1.32735 | ||||||||||||||||||
1.10 | −1.00000 | −1.47729 | 1.00000 | 2.55278 | 1.47729 | −3.54262 | −1.00000 | −0.817604 | −2.55278 | ||||||||||||||||||
1.11 | −1.00000 | −1.46112 | 1.00000 | 2.24970 | 1.46112 | −0.440676 | −1.00000 | −0.865116 | −2.24970 | ||||||||||||||||||
1.12 | −1.00000 | −0.987482 | 1.00000 | −4.26130 | 0.987482 | 0.584751 | −1.00000 | −2.02488 | 4.26130 | ||||||||||||||||||
1.13 | −1.00000 | −0.968563 | 1.00000 | −0.0731928 | 0.968563 | −0.501115 | −1.00000 | −2.06189 | 0.0731928 | ||||||||||||||||||
1.14 | −1.00000 | −0.909549 | 1.00000 | 0.734986 | 0.909549 | 5.27401 | −1.00000 | −2.17272 | −0.734986 | ||||||||||||||||||
1.15 | −1.00000 | −0.471999 | 1.00000 | 1.82038 | 0.471999 | −1.64482 | −1.00000 | −2.77722 | −1.82038 | ||||||||||||||||||
1.16 | −1.00000 | −0.0820624 | 1.00000 | −3.26458 | 0.0820624 | −0.430136 | −1.00000 | −2.99327 | 3.26458 | ||||||||||||||||||
1.17 | −1.00000 | 0.189963 | 1.00000 | 2.89176 | −0.189963 | 3.54124 | −1.00000 | −2.96391 | −2.89176 | ||||||||||||||||||
1.18 | −1.00000 | 0.214096 | 1.00000 | 2.53148 | −0.214096 | 4.82861 | −1.00000 | −2.95416 | −2.53148 | ||||||||||||||||||
1.19 | −1.00000 | 0.539204 | 1.00000 | −2.22740 | −0.539204 | 4.94386 | −1.00000 | −2.70926 | 2.22740 | ||||||||||||||||||
1.20 | −1.00000 | 0.581698 | 1.00000 | −2.21086 | −0.581698 | 1.23881 | −1.00000 | −2.66163 | 2.21086 | ||||||||||||||||||
See all 33 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.j | ✓ | 33 |
By twisted newform orbit | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Mult | Type |
6026.2.a.j | ✓ | 33 | 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 \(S_{2}^{\mathrm{new}}(\Gamma_0(6026))\):
\( T_{3}^{33} - 3 T_{3}^{32} - 67 T_{3}^{31} + 199 T_{3}^{30} + 2019 T_{3}^{29} - 5910 T_{3}^{28} - 36253 T_{3}^{27} + 103878 T_{3}^{26} + 433361 T_{3}^{25} - 1203529 T_{3}^{24} - 3650865 T_{3}^{23} + 9688729 T_{3}^{22} + \cdots - 92016 \) |
\( T_{5}^{33} + 4 T_{5}^{32} - 99 T_{5}^{31} - 389 T_{5}^{30} + 4393 T_{5}^{29} + 16959 T_{5}^{28} - 115344 T_{5}^{27} - 438324 T_{5}^{26} + 1991845 T_{5}^{25} + 7484524 T_{5}^{24} - 23774155 T_{5}^{23} + \cdots + 5425110 \) |