Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [6017,2,Mod(1,6017)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(6017, 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("6017.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 6017 = 11 \cdot 547 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 6017.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: | \(48.0459868962\) |
Analytic rank: | \(1\) |
Dimension: | \(107\) |
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 | −2.75999 | −3.06184 | 5.61754 | −2.40388 | 8.45065 | −3.94507 | −9.98436 | 6.37487 | 6.63467 | ||||||||||||||||||
1.2 | −2.74218 | −0.127111 | 5.51953 | 0.930528 | 0.348561 | −1.52234 | −9.65117 | −2.98384 | −2.55167 | ||||||||||||||||||
1.3 | −2.62131 | 1.98857 | 4.87127 | −3.39892 | −5.21266 | −2.62575 | −7.52650 | 0.954412 | 8.90963 | ||||||||||||||||||
1.4 | −2.60586 | −1.61281 | 4.79053 | 1.44359 | 4.20277 | 4.40298 | −7.27174 | −0.398838 | −3.76179 | ||||||||||||||||||
1.5 | −2.59133 | 1.08669 | 4.71497 | 2.54775 | −2.81596 | −0.206322 | −7.03537 | −1.81911 | −6.60204 | ||||||||||||||||||
1.6 | −2.52748 | −3.01490 | 4.38814 | 1.64213 | 7.62008 | 3.19622 | −6.03597 | 6.08959 | −4.15044 | ||||||||||||||||||
1.7 | −2.41913 | 2.57679 | 3.85218 | −1.00520 | −6.23359 | 1.76420 | −4.48067 | 3.63986 | 2.43171 | ||||||||||||||||||
1.8 | −2.41316 | −1.13111 | 3.82334 | 3.33661 | 2.72954 | −4.21510 | −4.40000 | −1.72060 | −8.05177 | ||||||||||||||||||
1.9 | −2.40409 | −1.43849 | 3.77967 | −1.50400 | 3.45826 | 0.877876 | −4.27850 | −0.930757 | 3.61576 | ||||||||||||||||||
1.10 | −2.38163 | −3.08400 | 3.67215 | 2.12353 | 7.34495 | −4.46240 | −3.98245 | 6.51107 | −5.05746 | ||||||||||||||||||
1.11 | −2.34564 | 1.00441 | 3.50205 | 3.21165 | −2.35600 | 2.32596 | −3.52327 | −1.99115 | −7.53339 | ||||||||||||||||||
1.12 | −2.29221 | −1.10986 | 3.25421 | −2.25000 | 2.54402 | −3.87042 | −2.87492 | −1.76822 | 5.15746 | ||||||||||||||||||
1.13 | −2.27956 | 2.53160 | 3.19638 | −2.07837 | −5.77093 | −1.61665 | −2.72721 | 3.40901 | 4.73776 | ||||||||||||||||||
1.14 | −2.25361 | −2.32484 | 3.07875 | −3.74526 | 5.23928 | −1.13542 | −2.43109 | 2.40489 | 8.44036 | ||||||||||||||||||
1.15 | −2.23665 | 0.286457 | 3.00262 | −1.07868 | −0.640706 | −2.04238 | −2.24251 | −2.91794 | 2.41263 | ||||||||||||||||||
1.16 | −2.18792 | 2.65305 | 2.78699 | 0.440982 | −5.80465 | 2.17034 | −1.72186 | 4.03866 | −0.964832 | ||||||||||||||||||
1.17 | −2.16456 | 1.81828 | 2.68531 | 1.50320 | −3.93577 | −2.76616 | −1.48340 | 0.306139 | −3.25377 | ||||||||||||||||||
1.18 | −2.10238 | 0.723159 | 2.42000 | −4.03444 | −1.52035 | 0.772372 | −0.882990 | −2.47704 | 8.48191 | ||||||||||||||||||
1.19 | −2.03276 | −2.20432 | 2.13212 | 2.54068 | 4.48086 | 2.78766 | −0.268560 | 1.85904 | −5.16459 | ||||||||||||||||||
1.20 | −1.94021 | −0.488619 | 1.76440 | −3.27450 | 0.948022 | −5.11134 | 0.457109 | −2.76125 | 6.35321 | ||||||||||||||||||
See next 80 embeddings (of 107 total) |
Atkin-Lehner signs
\( p \) | Sign |
---|---|
\(11\) | \(1\) |
\(547\) | \(1\) |
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 | 6017.2.a.d | ✓ | 107 |
By twisted newform orbit | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Mult | Type |
6017.2.a.d | ✓ | 107 | 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 \(S_{2}^{\mathrm{new}}(\Gamma_0(6017))\):
\( T_{2}^{107} + 3 T_{2}^{106} - 148 T_{2}^{105} - 448 T_{2}^{104} + 10594 T_{2}^{103} + 32379 T_{2}^{102} - 488643 T_{2}^{101} - 1509048 T_{2}^{100} + 16324926 T_{2}^{99} + 50982788 T_{2}^{98} - 421009081 T_{2}^{97} + \cdots - 19904 \) |
\( T_{3}^{107} + 18 T_{3}^{106} - 46 T_{3}^{105} - 2717 T_{3}^{104} - 7408 T_{3}^{103} + 187989 T_{3}^{102} + 1025495 T_{3}^{101} - 7677676 T_{3}^{100} - 64496240 T_{3}^{99} + 190707793 T_{3}^{98} + \cdots - 2485795611644 \) |