Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [6019,2,Mod(1,6019)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(6019, 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("6019.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 6019 = 13 \cdot 463 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 6019.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: | \(48.0619569766\) |
Analytic rank: | \(1\) |
Dimension: | \(101\) |
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 | −2.77092 | −0.383319 | 5.67797 | −1.00861 | 1.06214 | 0.495501 | −10.1914 | −2.85307 | 2.79476 | ||||||||||||||||||
1.2 | −2.75200 | 0.205353 | 5.57349 | −1.15382 | −0.565131 | 4.79173 | −9.83422 | −2.95783 | 3.17530 | ||||||||||||||||||
1.3 | −2.66557 | −0.463578 | 5.10529 | 3.99027 | 1.23570 | −1.40213 | −8.27737 | −2.78510 | −10.6364 | ||||||||||||||||||
1.4 | −2.61088 | −2.81902 | 4.81671 | −3.25148 | 7.36014 | 3.68170 | −7.35411 | 4.94689 | 8.48923 | ||||||||||||||||||
1.5 | −2.59744 | 2.60815 | 4.74669 | −0.0717768 | −6.77450 | 0.808846 | −7.13437 | 3.80242 | 0.186436 | ||||||||||||||||||
1.6 | −2.53156 | 1.58470 | 4.40878 | 2.52136 | −4.01175 | −1.30202 | −6.09798 | −0.488741 | −6.38296 | ||||||||||||||||||
1.7 | −2.51903 | 1.84872 | 4.34553 | −3.50196 | −4.65699 | 1.30916 | −5.90847 | 0.417768 | 8.82155 | ||||||||||||||||||
1.8 | −2.47893 | −2.41040 | 4.14507 | 2.56792 | 5.97521 | 2.73390 | −5.31747 | 2.81004 | −6.36569 | ||||||||||||||||||
1.9 | −2.44907 | −1.63543 | 3.99796 | −2.35876 | 4.00528 | 1.29431 | −4.89316 | −0.325384 | 5.77678 | ||||||||||||||||||
1.10 | −2.35123 | −2.62167 | 3.52828 | −1.32904 | 6.16416 | −2.62369 | −3.59334 | 3.87318 | 3.12489 | ||||||||||||||||||
1.11 | −2.33786 | −0.380371 | 3.46560 | −3.85216 | 0.889254 | −3.60381 | −3.42637 | −2.85532 | 9.00581 | ||||||||||||||||||
1.12 | −2.32242 | 2.86947 | 3.39365 | 0.571930 | −6.66413 | −0.979167 | −3.23665 | 5.23387 | −1.32826 | ||||||||||||||||||
1.13 | −2.31630 | 0.457851 | 3.36526 | 2.03378 | −1.06052 | 1.32033 | −3.16236 | −2.79037 | −4.71086 | ||||||||||||||||||
1.14 | −2.22409 | −1.49293 | 2.94657 | −0.404702 | 3.32042 | −4.24821 | −2.10525 | −0.771146 | 0.900094 | ||||||||||||||||||
1.15 | −2.18475 | 1.46102 | 2.77312 | −4.12132 | −3.19197 | 2.89283 | −1.68907 | −0.865408 | 9.00405 | ||||||||||||||||||
1.16 | −2.11661 | 2.26026 | 2.48003 | −0.342197 | −4.78408 | 3.30081 | −1.01604 | 2.10876 | 0.724298 | ||||||||||||||||||
1.17 | −2.06993 | −2.73222 | 2.28462 | 1.87227 | 5.65552 | −2.93607 | −0.589152 | 4.46505 | −3.87547 | ||||||||||||||||||
1.18 | −2.04146 | 1.76541 | 2.16756 | −1.03624 | −3.60401 | −3.97509 | −0.342069 | 0.116656 | 2.11544 | ||||||||||||||||||
1.19 | −2.03639 | −1.20777 | 2.14690 | 3.16451 | 2.45949 | 3.67207 | −0.299141 | −1.54130 | −6.44419 | ||||||||||||||||||
1.20 | −1.88082 | −1.45946 | 1.53747 | 1.38464 | 2.74498 | −0.844871 | 0.869931 | −0.869978 | −2.60424 | ||||||||||||||||||
See next 80 embeddings (of 101 total) |
Atkin-Lehner signs
\( p \) | Sign |
---|---|
\(13\) | \(-1\) |
\(463\) | \(-1\) |
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 | 6019.2.a.b | ✓ | 101 |
By twisted newform orbit | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Mult | Type |
6019.2.a.b | ✓ | 101 | 1.a | even | 1 | 1 | trivial |
Hecke kernels
This newform subspace can be constructed as the kernel of the linear operator \( T_{2}^{101} + 8 T_{2}^{100} - 112 T_{2}^{99} - 1048 T_{2}^{98} + 5737 T_{2}^{97} + 66172 T_{2}^{96} + \cdots - 25589025 \) acting on \(S_{2}^{\mathrm{new}}(\Gamma_0(6019))\).