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: | \(25\) |
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 | −2.98476 | 1.00000 | 1.57995 | 2.98476 | 2.90984 | −1.00000 | 5.90879 | −1.57995 | ||||||||||||||||||
1.2 | −1.00000 | −2.94469 | 1.00000 | −3.10338 | 2.94469 | 2.18728 | −1.00000 | 5.67118 | 3.10338 | ||||||||||||||||||
1.3 | −1.00000 | −2.94225 | 1.00000 | 2.28313 | 2.94225 | −4.71427 | −1.00000 | 5.65684 | −2.28313 | ||||||||||||||||||
1.4 | −1.00000 | −2.39972 | 1.00000 | 1.46275 | 2.39972 | 0.813594 | −1.00000 | 2.75865 | −1.46275 | ||||||||||||||||||
1.5 | −1.00000 | −2.37203 | 1.00000 | 3.53118 | 2.37203 | −2.86520 | −1.00000 | 2.62654 | −3.53118 | ||||||||||||||||||
1.6 | −1.00000 | −2.34651 | 1.00000 | −0.801214 | 2.34651 | 2.16934 | −1.00000 | 2.50610 | 0.801214 | ||||||||||||||||||
1.7 | −1.00000 | −1.97733 | 1.00000 | −3.11644 | 1.97733 | −3.94255 | −1.00000 | 0.909824 | 3.11644 | ||||||||||||||||||
1.8 | −1.00000 | −1.70631 | 1.00000 | −2.14849 | 1.70631 | 0.462300 | −1.00000 | −0.0885110 | 2.14849 | ||||||||||||||||||
1.9 | −1.00000 | −1.05724 | 1.00000 | −2.13811 | 1.05724 | 3.42578 | −1.00000 | −1.88224 | 2.13811 | ||||||||||||||||||
1.10 | −1.00000 | −0.936776 | 1.00000 | 1.38125 | 0.936776 | 2.49293 | −1.00000 | −2.12245 | −1.38125 | ||||||||||||||||||
1.11 | −1.00000 | −0.932148 | 1.00000 | −0.513090 | 0.932148 | 0.0983188 | −1.00000 | −2.13110 | 0.513090 | ||||||||||||||||||
1.12 | −1.00000 | −0.665355 | 1.00000 | 0.670202 | 0.665355 | −3.39786 | −1.00000 | −2.55730 | −0.670202 | ||||||||||||||||||
1.13 | −1.00000 | −0.0412722 | 1.00000 | −3.47552 | 0.0412722 | −4.67489 | −1.00000 | −2.99830 | 3.47552 | ||||||||||||||||||
1.14 | −1.00000 | 0.180068 | 1.00000 | −3.11636 | −0.180068 | 2.83625 | −1.00000 | −2.96758 | 3.11636 | ||||||||||||||||||
1.15 | −1.00000 | 0.489389 | 1.00000 | 2.70694 | −0.489389 | 1.75684 | −1.00000 | −2.76050 | −2.70694 | ||||||||||||||||||
1.16 | −1.00000 | 0.694821 | 1.00000 | 0.658132 | −0.694821 | −2.75018 | −1.00000 | −2.51722 | −0.658132 | ||||||||||||||||||
1.17 | −1.00000 | 0.888297 | 1.00000 | 2.86945 | −0.888297 | −2.14877 | −1.00000 | −2.21093 | −2.86945 | ||||||||||||||||||
1.18 | −1.00000 | 1.11977 | 1.00000 | 0.636447 | −1.11977 | 1.86618 | −1.00000 | −1.74612 | −0.636447 | ||||||||||||||||||
1.19 | −1.00000 | 1.50502 | 1.00000 | −2.72563 | −1.50502 | −2.36491 | −1.00000 | −0.734912 | 2.72563 | ||||||||||||||||||
1.20 | −1.00000 | 1.76687 | 1.00000 | −0.379310 | −1.76687 | −0.00141487 | −1.00000 | 0.121841 | 0.379310 | ||||||||||||||||||
See all 25 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.i | ✓ | 25 |
By twisted newform orbit | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Mult | Type |
6026.2.a.i | ✓ | 25 | 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 \(S_{2}^{\mathrm{new}}(\Gamma_0(6026))\):
\( T_{3}^{25} + 4 T_{3}^{24} - 39 T_{3}^{23} - 165 T_{3}^{22} + 640 T_{3}^{21} + 2914 T_{3}^{20} + \cdots + 480 \) |
\( T_{5}^{25} + 3 T_{5}^{24} - 60 T_{5}^{23} - 174 T_{5}^{22} + 1566 T_{5}^{21} + 4330 T_{5}^{20} + \cdots + 211472 \) |