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: | \(24\) |
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 | −3.27057 | 1.00000 | −0.103796 | 3.27057 | 0.553111 | −1.00000 | 7.69663 | 0.103796 | ||||||||||||||||||
1.2 | −1.00000 | −3.03806 | 1.00000 | 2.76911 | 3.03806 | −0.589865 | −1.00000 | 6.22984 | −2.76911 | ||||||||||||||||||
1.3 | −1.00000 | −2.99000 | 1.00000 | −3.60098 | 2.99000 | 0.0770196 | −1.00000 | 5.94012 | 3.60098 | ||||||||||||||||||
1.4 | −1.00000 | −2.41227 | 1.00000 | 0.460247 | 2.41227 | −4.49457 | −1.00000 | 2.81904 | −0.460247 | ||||||||||||||||||
1.5 | −1.00000 | −2.26660 | 1.00000 | 3.87731 | 2.26660 | 1.72764 | −1.00000 | 2.13746 | −3.87731 | ||||||||||||||||||
1.6 | −1.00000 | −1.90388 | 1.00000 | −1.40322 | 1.90388 | −1.81515 | −1.00000 | 0.624755 | 1.40322 | ||||||||||||||||||
1.7 | −1.00000 | −1.71989 | 1.00000 | −2.14325 | 1.71989 | −1.30637 | −1.00000 | −0.0419677 | 2.14325 | ||||||||||||||||||
1.8 | −1.00000 | −1.04677 | 1.00000 | 3.02542 | 1.04677 | −3.14954 | −1.00000 | −1.90427 | −3.02542 | ||||||||||||||||||
1.9 | −1.00000 | −0.985760 | 1.00000 | −1.64046 | 0.985760 | −3.55255 | −1.00000 | −2.02828 | 1.64046 | ||||||||||||||||||
1.10 | −1.00000 | −0.785811 | 1.00000 | −1.42219 | 0.785811 | 3.87369 | −1.00000 | −2.38250 | 1.42219 | ||||||||||||||||||
1.11 | −1.00000 | −0.672761 | 1.00000 | −2.38352 | 0.672761 | −0.506434 | −1.00000 | −2.54739 | 2.38352 | ||||||||||||||||||
1.12 | −1.00000 | −0.666016 | 1.00000 | 0.513693 | 0.666016 | 2.90198 | −1.00000 | −2.55642 | −0.513693 | ||||||||||||||||||
1.13 | −1.00000 | −0.510961 | 1.00000 | 2.36930 | 0.510961 | 2.78886 | −1.00000 | −2.73892 | −2.36930 | ||||||||||||||||||
1.14 | −1.00000 | 0.562960 | 1.00000 | −3.89005 | −0.562960 | −0.867650 | −1.00000 | −2.68308 | 3.89005 | ||||||||||||||||||
1.15 | −1.00000 | 0.977360 | 1.00000 | 1.34259 | −0.977360 | −1.08765 | −1.00000 | −2.04477 | −1.34259 | ||||||||||||||||||
1.16 | −1.00000 | 1.11947 | 1.00000 | 1.71773 | −1.11947 | 3.78646 | −1.00000 | −1.74680 | −1.71773 | ||||||||||||||||||
1.17 | −1.00000 | 1.48980 | 1.00000 | 3.56615 | −1.48980 | −2.69745 | −1.00000 | −0.780502 | −3.56615 | ||||||||||||||||||
1.18 | −1.00000 | 1.66164 | 1.00000 | 0.0681057 | −1.66164 | 0.103168 | −1.00000 | −0.238964 | −0.0681057 | ||||||||||||||||||
1.19 | −1.00000 | 1.72713 | 1.00000 | 0.546511 | −1.72713 | 2.37970 | −1.00000 | −0.0170298 | −0.546511 | ||||||||||||||||||
1.20 | −1.00000 | 2.29919 | 1.00000 | −1.62268 | −2.29919 | −0.601158 | −1.00000 | 2.28626 | 1.62268 | ||||||||||||||||||
See all 24 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.h | ✓ | 24 |
By twisted newform orbit | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Mult | Type |
6026.2.a.h | ✓ | 24 | 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 \(S_{2}^{\mathrm{new}}(\Gamma_0(6026))\):
\( T_{3}^{24} + T_{3}^{23} - 49 T_{3}^{22} - 47 T_{3}^{21} + 1028 T_{3}^{20} + 951 T_{3}^{19} + \cdots - 39168 \) |
\( T_{5}^{24} + T_{5}^{23} - 60 T_{5}^{22} - 59 T_{5}^{21} + 1511 T_{5}^{20} + 1444 T_{5}^{19} + \cdots - 1728 \) |