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: | \(106\) |
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 | −2.78235 | −0.369906 | 5.74149 | −3.02150 | 1.02921 | −3.23246 | −10.4101 | −2.86317 | 8.40687 | ||||||||||||||||||
1.2 | −2.76753 | −2.67959 | 5.65924 | 2.34491 | 7.41585 | −2.59530 | −10.1271 | 4.18020 | −6.48960 | ||||||||||||||||||
1.3 | −2.73187 | −0.157601 | 5.46313 | 2.56928 | 0.430546 | −5.24072 | −9.46082 | −2.97516 | −7.01894 | ||||||||||||||||||
1.4 | −2.70820 | 2.96568 | 5.33437 | −1.26109 | −8.03167 | 1.85077 | −9.03015 | 5.79526 | 3.41529 | ||||||||||||||||||
1.5 | −2.66450 | 0.632884 | 5.09957 | −0.0737087 | −1.68632 | 1.42532 | −8.25880 | −2.59946 | 0.196397 | ||||||||||||||||||
1.6 | −2.61585 | 1.81779 | 4.84270 | 3.74717 | −4.75507 | 0.406260 | −7.43608 | 0.304348 | −9.80206 | ||||||||||||||||||
1.7 | −2.58511 | −2.87890 | 4.68281 | −1.51557 | 7.44229 | 0.161489 | −6.93538 | 5.28808 | 3.91792 | ||||||||||||||||||
1.8 | −2.57284 | 2.82606 | 4.61950 | 1.34186 | −7.27099 | −3.61511 | −6.73954 | 4.98661 | −3.45239 | ||||||||||||||||||
1.9 | −2.47702 | 3.19961 | 4.13562 | −3.89998 | −7.92550 | −4.57915 | −5.28996 | 7.23752 | 9.66032 | ||||||||||||||||||
1.10 | −2.43520 | −0.763891 | 3.93019 | 1.56797 | 1.86023 | 2.19104 | −4.70040 | −2.41647 | −3.81832 | ||||||||||||||||||
1.11 | −2.42329 | −0.918445 | 3.87233 | −2.10804 | 2.22566 | −2.69568 | −4.53719 | −2.15646 | 5.10839 | ||||||||||||||||||
1.12 | −2.39408 | −0.179689 | 3.73161 | −1.83517 | 0.430189 | 0.373924 | −4.14560 | −2.96771 | 4.39353 | ||||||||||||||||||
1.13 | −2.37596 | 1.38475 | 3.64518 | 0.740241 | −3.29011 | −0.0236528 | −3.90889 | −1.08246 | −1.75878 | ||||||||||||||||||
1.14 | −2.32740 | −3.07559 | 3.41677 | −1.26158 | 7.15812 | 0.599145 | −3.29739 | 6.45928 | 2.93620 | ||||||||||||||||||
1.15 | −2.32398 | −3.12042 | 3.40089 | 3.91464 | 7.25180 | −0.989043 | −3.25564 | 6.73703 | −9.09756 | ||||||||||||||||||
1.16 | −2.18387 | 1.05356 | 2.76930 | 1.41364 | −2.30083 | 4.87614 | −1.68005 | −1.89002 | −3.08721 | ||||||||||||||||||
1.17 | −2.16812 | −0.750565 | 2.70073 | −2.22726 | 1.62731 | 3.66777 | −1.51925 | −2.43665 | 4.82897 | ||||||||||||||||||
1.18 | −2.11348 | −1.48934 | 2.46682 | 2.94089 | 3.14770 | 2.33045 | −0.986611 | −0.781868 | −6.21552 | ||||||||||||||||||
1.19 | −2.01004 | −2.26087 | 2.04024 | −3.50443 | 4.54443 | 2.31355 | −0.0808885 | 2.11154 | 7.04404 | ||||||||||||||||||
1.20 | −1.99930 | −0.450091 | 1.99721 | 2.88473 | 0.899867 | −0.362986 | 0.00557515 | −2.79742 | −5.76745 | ||||||||||||||||||
See next 80 embeddings (of 106 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.c | ✓ | 106 |
By twisted newform orbit | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Mult | Type |
6017.2.a.c | ✓ | 106 | 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 \(S_{2}^{\mathrm{new}}(\Gamma_0(6017))\):
\( T_{2}^{106} + 13 T_{2}^{105} - 68 T_{2}^{104} - 1586 T_{2}^{103} - 44 T_{2}^{102} + 91677 T_{2}^{101} + \cdots - 180152 \) |
\( T_{3}^{106} + 15 T_{3}^{105} - 95 T_{3}^{104} - 2502 T_{3}^{103} + 290 T_{3}^{102} + 197423 T_{3}^{101} + \cdots + 9726334200 \) |