Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [6033,2,Mod(1,6033)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(6033, 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("6033.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 6033 = 3 \cdot 2011 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 6033.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: | \(48.1737475394\) |
Analytic rank: | \(1\) |
Dimension: | \(84\) |
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 | −2.82117 | −1.00000 | 5.95898 | −2.46990 | 2.82117 | 0.575292 | −11.1689 | 1.00000 | 6.96801 | ||||||||||||||||||
1.2 | −2.80639 | −1.00000 | 5.87581 | 1.59554 | 2.80639 | −1.53809 | −10.8770 | 1.00000 | −4.47769 | ||||||||||||||||||
1.3 | −2.73519 | −1.00000 | 5.48127 | −2.75382 | 2.73519 | −2.09506 | −9.52192 | 1.00000 | 7.53221 | ||||||||||||||||||
1.4 | −2.66273 | −1.00000 | 5.09011 | 2.84840 | 2.66273 | −4.34717 | −8.22811 | 1.00000 | −7.58450 | ||||||||||||||||||
1.5 | −2.60952 | −1.00000 | 4.80961 | 2.15432 | 2.60952 | −3.44517 | −7.33175 | 1.00000 | −5.62175 | ||||||||||||||||||
1.6 | −2.60855 | −1.00000 | 4.80454 | −1.00742 | 2.60855 | 3.22569 | −7.31578 | 1.00000 | 2.62791 | ||||||||||||||||||
1.7 | −2.59128 | −1.00000 | 4.71472 | −3.30142 | 2.59128 | 3.98473 | −7.03459 | 1.00000 | 8.55491 | ||||||||||||||||||
1.8 | −2.57191 | −1.00000 | 4.61473 | 2.62462 | 2.57191 | 3.44877 | −6.72487 | 1.00000 | −6.75028 | ||||||||||||||||||
1.9 | −2.45280 | −1.00000 | 4.01624 | −4.16660 | 2.45280 | −2.71400 | −4.94544 | 1.00000 | 10.2199 | ||||||||||||||||||
1.10 | −2.42494 | −1.00000 | 3.88033 | −3.57030 | 2.42494 | 1.93625 | −4.55968 | 1.00000 | 8.65775 | ||||||||||||||||||
1.11 | −2.41532 | −1.00000 | 3.83378 | −1.96861 | 2.41532 | −4.53404 | −4.42916 | 1.00000 | 4.75483 | ||||||||||||||||||
1.12 | −2.31178 | −1.00000 | 3.34433 | 1.56630 | 2.31178 | 1.68307 | −3.10780 | 1.00000 | −3.62093 | ||||||||||||||||||
1.13 | −2.22564 | −1.00000 | 2.95347 | −0.168445 | 2.22564 | −0.580440 | −2.12207 | 1.00000 | 0.374898 | ||||||||||||||||||
1.14 | −2.16814 | −1.00000 | 2.70083 | 3.39119 | 2.16814 | 2.22873 | −1.51950 | 1.00000 | −7.35257 | ||||||||||||||||||
1.15 | −2.10715 | −1.00000 | 2.44009 | 0.912218 | 2.10715 | 4.59060 | −0.927338 | 1.00000 | −1.92218 | ||||||||||||||||||
1.16 | −2.06135 | −1.00000 | 2.24917 | −2.50323 | 2.06135 | 1.09494 | −0.513635 | 1.00000 | 5.16004 | ||||||||||||||||||
1.17 | −2.02957 | −1.00000 | 2.11915 | 3.74775 | 2.02957 | −1.06025 | −0.241816 | 1.00000 | −7.60631 | ||||||||||||||||||
1.18 | −2.00535 | −1.00000 | 2.02142 | 2.82902 | 2.00535 | −3.36485 | −0.0429452 | 1.00000 | −5.67317 | ||||||||||||||||||
1.19 | −1.86532 | −1.00000 | 1.47943 | −0.830382 | 1.86532 | −1.56075 | 0.971032 | 1.00000 | 1.54893 | ||||||||||||||||||
1.20 | −1.84665 | −1.00000 | 1.41011 | −1.36043 | 1.84665 | −4.64728 | 1.08932 | 1.00000 | 2.51223 | ||||||||||||||||||
See all 84 embeddings |
Atkin-Lehner signs
\( p \) | Sign |
---|---|
\(3\) | \(1\) |
\(2011\) | \(1\) |
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 | 6033.2.a.d | ✓ | 84 |
By twisted newform orbit | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Mult | Type |
6033.2.a.d | ✓ | 84 | 1.a | even | 1 | 1 | trivial |
Hecke kernels
This newform subspace can be constructed as the kernel of the linear operator \( T_{2}^{84} + 13 T_{2}^{83} - 40 T_{2}^{82} - 1222 T_{2}^{81} - 1496 T_{2}^{80} + 53145 T_{2}^{79} + \cdots + 367488 \) acting on \(S_{2}^{\mathrm{new}}(\Gamma_0(6033))\).