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: | \(35\) |
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 | −3.43871 | 1.00000 | −4.28403 | −3.43871 | 1.96690 | 1.00000 | 8.82470 | −4.28403 | ||||||||||||||||||
1.2 | 1.00000 | −3.36223 | 1.00000 | 2.69270 | −3.36223 | −4.35375 | 1.00000 | 8.30456 | 2.69270 | ||||||||||||||||||
1.3 | 1.00000 | −3.00053 | 1.00000 | 0.314170 | −3.00053 | 4.93238 | 1.00000 | 6.00320 | 0.314170 | ||||||||||||||||||
1.4 | 1.00000 | −2.88440 | 1.00000 | 3.48712 | −2.88440 | 4.69814 | 1.00000 | 5.31979 | 3.48712 | ||||||||||||||||||
1.5 | 1.00000 | −2.84834 | 1.00000 | 3.81635 | −2.84834 | −2.03504 | 1.00000 | 5.11302 | 3.81635 | ||||||||||||||||||
1.6 | 1.00000 | −2.77524 | 1.00000 | −2.60760 | −2.77524 | −2.68280 | 1.00000 | 4.70196 | −2.60760 | ||||||||||||||||||
1.7 | 1.00000 | −2.41881 | 1.00000 | −3.09594 | −2.41881 | 0.393889 | 1.00000 | 2.85065 | −3.09594 | ||||||||||||||||||
1.8 | 1.00000 | −2.41686 | 1.00000 | −1.19985 | −2.41686 | −1.78090 | 1.00000 | 2.84122 | −1.19985 | ||||||||||||||||||
1.9 | 1.00000 | −2.05490 | 1.00000 | 0.786161 | −2.05490 | −2.31145 | 1.00000 | 1.22260 | 0.786161 | ||||||||||||||||||
1.10 | 1.00000 | −1.74363 | 1.00000 | 1.36417 | −1.74363 | 0.246249 | 1.00000 | 0.0402388 | 1.36417 | ||||||||||||||||||
1.11 | 1.00000 | −1.69112 | 1.00000 | −3.34531 | −1.69112 | 0.398747 | 1.00000 | −0.140113 | −3.34531 | ||||||||||||||||||
1.12 | 1.00000 | −1.65659 | 1.00000 | −0.00351955 | −1.65659 | −4.74512 | 1.00000 | −0.255700 | −0.00351955 | ||||||||||||||||||
1.13 | 1.00000 | −1.52794 | 1.00000 | 1.80988 | −1.52794 | 2.28195 | 1.00000 | −0.665396 | 1.80988 | ||||||||||||||||||
1.14 | 1.00000 | −0.824185 | 1.00000 | 2.25531 | −0.824185 | 4.15544 | 1.00000 | −2.32072 | 2.25531 | ||||||||||||||||||
1.15 | 1.00000 | −0.783973 | 1.00000 | 4.00344 | −0.783973 | 0.255131 | 1.00000 | −2.38539 | 4.00344 | ||||||||||||||||||
1.16 | 1.00000 | −0.711607 | 1.00000 | −3.74432 | −0.711607 | 2.05633 | 1.00000 | −2.49362 | −3.74432 | ||||||||||||||||||
1.17 | 1.00000 | −0.339838 | 1.00000 | −2.83329 | −0.339838 | −3.26036 | 1.00000 | −2.88451 | −2.83329 | ||||||||||||||||||
1.18 | 1.00000 | 0.0639197 | 1.00000 | 0.144901 | 0.0639197 | −1.36969 | 1.00000 | −2.99591 | 0.144901 | ||||||||||||||||||
1.19 | 1.00000 | 0.0851442 | 1.00000 | −0.378458 | 0.0851442 | 4.38766 | 1.00000 | −2.99275 | −0.378458 | ||||||||||||||||||
1.20 | 1.00000 | 0.671472 | 1.00000 | 3.81346 | 0.671472 | 3.17342 | 1.00000 | −2.54913 | 3.81346 | ||||||||||||||||||
See all 35 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.k | ✓ | 35 |
By twisted newform orbit | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Mult | Type |
6026.2.a.k | ✓ | 35 | 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 \(S_{2}^{\mathrm{new}}(\Gamma_0(6026))\):
\( T_{3}^{35} + 3 T_{3}^{34} - 75 T_{3}^{33} - 221 T_{3}^{32} + 2549 T_{3}^{31} + 7362 T_{3}^{30} - 51953 T_{3}^{29} - 146684 T_{3}^{28} + 708385 T_{3}^{27} + 1948411 T_{3}^{26} - 6827279 T_{3}^{25} - 18207157 T_{3}^{24} + \cdots + 336640 \) |
\( T_{5}^{35} - 10 T_{5}^{34} - 78 T_{5}^{33} + 1077 T_{5}^{32} + 1791 T_{5}^{31} - 50978 T_{5}^{30} + 24035 T_{5}^{29} + 1394260 T_{5}^{28} - 2305664 T_{5}^{27} - 24321424 T_{5}^{26} + 61493531 T_{5}^{25} + \cdots - 4543552 \) |