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: | \(108\) |
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 | −2.77848 | 2.29765 | 5.71995 | 2.18323 | −6.38396 | 0.752947 | −10.3358 | 2.27917 | −6.06605 | ||||||||||||||||||
1.2 | −2.73685 | −2.13610 | 5.49032 | −3.88543 | 5.84618 | −1.04170 | −9.55248 | 1.56292 | 10.6338 | ||||||||||||||||||
1.3 | −2.64969 | −0.413927 | 5.02086 | −1.95969 | 1.09678 | −0.899778 | −8.00435 | −2.82866 | 5.19257 | ||||||||||||||||||
1.4 | −2.62932 | 0.928194 | 4.91333 | 1.81764 | −2.44052 | 3.79843 | −7.66009 | −2.13846 | −4.77917 | ||||||||||||||||||
1.5 | −2.62196 | −0.813055 | 4.87469 | 0.562087 | 2.13180 | −5.01388 | −7.53732 | −2.33894 | −1.47377 | ||||||||||||||||||
1.6 | −2.61467 | 0.516414 | 4.83649 | −3.96792 | −1.35025 | 3.66433 | −7.41648 | −2.73332 | 10.3748 | ||||||||||||||||||
1.7 | −2.60952 | 3.26666 | 4.80961 | −2.76749 | −8.52442 | −0.615812 | −7.33173 | 7.67107 | 7.22184 | ||||||||||||||||||
1.8 | −2.59599 | 1.19783 | 4.73919 | −2.90334 | −3.10956 | −3.26881 | −7.11092 | −1.56520 | 7.53704 | ||||||||||||||||||
1.9 | −2.56322 | −2.39331 | 4.57009 | 1.98047 | 6.13457 | 1.46442 | −6.58772 | 2.72791 | −5.07639 | ||||||||||||||||||
1.10 | −2.51181 | −2.99105 | 4.30921 | 1.76112 | 7.51295 | 3.89256 | −5.80031 | 5.94635 | −4.42360 | ||||||||||||||||||
1.11 | −2.39631 | −0.467815 | 3.74231 | 2.01057 | 1.12103 | −2.84779 | −4.17511 | −2.78115 | −4.81795 | ||||||||||||||||||
1.12 | −2.34535 | −1.65067 | 3.50065 | −1.17678 | 3.87140 | 2.05341 | −3.51955 | −0.275278 | 2.75996 | ||||||||||||||||||
1.13 | −2.34425 | −1.25776 | 3.49550 | −1.49624 | 2.94851 | 5.17811 | −3.50582 | −1.41803 | 3.50756 | ||||||||||||||||||
1.14 | −2.26345 | 2.92995 | 3.12323 | 0.680242 | −6.63181 | −3.22192 | −2.54237 | 5.58462 | −1.53970 | ||||||||||||||||||
1.15 | −2.25939 | 2.42736 | 3.10485 | −0.500622 | −5.48435 | 4.41326 | −2.49629 | 2.89206 | 1.13110 | ||||||||||||||||||
1.16 | −2.23728 | 2.31482 | 3.00542 | −4.05108 | −5.17891 | −5.18040 | −2.24940 | 2.35841 | 9.06339 | ||||||||||||||||||
1.17 | −2.20802 | −2.87685 | 2.87536 | 1.19118 | 6.35214 | −0.105056 | −1.93280 | 5.27625 | −2.63016 | ||||||||||||||||||
1.18 | −2.18373 | 2.09330 | 2.76866 | 2.17810 | −4.57119 | −2.34745 | −1.67854 | 1.38190 | −4.75637 | ||||||||||||||||||
1.19 | −2.14163 | −1.26927 | 2.58656 | 2.68002 | 2.71830 | −0.999709 | −1.25619 | −1.38895 | −5.73960 | ||||||||||||||||||
1.20 | −2.12654 | −0.167601 | 2.52216 | −1.92531 | 0.356410 | 0.0410631 | −1.11038 | −2.97191 | 4.09424 | ||||||||||||||||||
See next 80 embeddings (of 108 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.c | ✓ | 108 |
By twisted newform orbit | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Mult | Type |
6019.2.a.c | ✓ | 108 | 1.a | even | 1 | 1 | trivial |
Hecke kernels
This newform subspace can be constructed as the kernel of the linear operator \( T_{2}^{108} + 11 T_{2}^{107} - 95 T_{2}^{106} - 1463 T_{2}^{105} + 3198 T_{2}^{104} + 93368 T_{2}^{103} + \cdots - 103242 \) acting on \(S_{2}^{\mathrm{new}}(\Gamma_0(6019))\).