Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [8033,2,Mod(1,8033)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(8033, 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("8033.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 8033 = 29 \cdot 277 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 8033.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: | \(64.1438279437\) |
Analytic rank: | \(0\) |
Dimension: | \(168\) |
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 | −2.81703 | 3.39159 | 5.93564 | −2.93306 | −9.55421 | 1.32517 | −11.0868 | 8.50291 | 8.26251 | ||||||||||||||||||
1.2 | −2.78974 | 1.21931 | 5.78265 | −2.52098 | −3.40156 | 3.27965 | −10.5526 | −1.51328 | 7.03288 | ||||||||||||||||||
1.3 | −2.72891 | 1.81680 | 5.44695 | 0.385312 | −4.95790 | −3.34669 | −9.40642 | 0.300780 | −1.05148 | ||||||||||||||||||
1.4 | −2.69929 | 0.546346 | 5.28617 | −1.10957 | −1.47475 | 1.76751 | −8.87031 | −2.70151 | 2.99504 | ||||||||||||||||||
1.5 | −2.69133 | −1.56780 | 5.24327 | 1.58955 | 4.21948 | −0.425755 | −8.72870 | −0.541992 | −4.27800 | ||||||||||||||||||
1.6 | −2.62201 | −2.34634 | 4.87492 | −4.13917 | 6.15213 | 1.37941 | −7.53807 | 2.50532 | 10.8529 | ||||||||||||||||||
1.7 | −2.58554 | −1.99550 | 4.68504 | 0.489761 | 5.15945 | 4.81577 | −6.94230 | 0.982009 | −1.26630 | ||||||||||||||||||
1.8 | −2.57726 | 2.47639 | 4.64228 | 3.37343 | −6.38231 | −1.62921 | −6.80985 | 3.13252 | −8.69420 | ||||||||||||||||||
1.9 | −2.53885 | 1.12516 | 4.44574 | −4.00247 | −2.85660 | 4.31591 | −6.20937 | −1.73402 | 10.1617 | ||||||||||||||||||
1.10 | −2.52738 | −1.64022 | 4.38763 | 1.90507 | 4.14544 | −1.36071 | −6.03443 | −0.309688 | −4.81483 | ||||||||||||||||||
1.11 | −2.52129 | 1.55242 | 4.35693 | 3.41413 | −3.91411 | 1.49471 | −5.94251 | −0.589992 | −8.60803 | ||||||||||||||||||
1.12 | −2.50804 | 0.217745 | 4.29026 | −0.0259578 | −0.546113 | −4.91509 | −5.74406 | −2.95259 | 0.0651033 | ||||||||||||||||||
1.13 | −2.50746 | −1.63037 | 4.28734 | 3.92256 | 4.08808 | 3.39028 | −5.73541 | −0.341901 | −9.83565 | ||||||||||||||||||
1.14 | −2.46662 | 2.34956 | 4.08421 | 0.440108 | −5.79546 | 2.07787 | −5.14095 | 2.52042 | −1.08558 | ||||||||||||||||||
1.15 | −2.44996 | −1.86877 | 4.00229 | −1.18542 | 4.57841 | −4.60968 | −4.90553 | 0.492307 | 2.90424 | ||||||||||||||||||
1.16 | −2.41744 | −0.0531053 | 3.84399 | −0.881470 | 0.128379 | 1.45309 | −4.45773 | −2.99718 | 2.13090 | ||||||||||||||||||
1.17 | −2.40677 | −1.38895 | 3.79253 | −2.91778 | 3.34287 | 3.15140 | −4.31420 | −1.07083 | 7.02241 | ||||||||||||||||||
1.18 | −2.40306 | 1.89974 | 3.77470 | −4.37204 | −4.56518 | −3.13994 | −4.26472 | 0.608994 | 10.5063 | ||||||||||||||||||
1.19 | −2.34777 | 0.405872 | 3.51204 | −3.82329 | −0.952896 | 0.144242 | −3.54992 | −2.83527 | 8.97621 | ||||||||||||||||||
1.20 | −2.33211 | 3.25701 | 3.43872 | 3.02617 | −7.59569 | 3.43735 | −3.35525 | 7.60809 | −7.05735 | ||||||||||||||||||
See next 80 embeddings (of 168 total) |
Atkin-Lehner signs
\( p \) | Sign |
---|---|
\(29\) | \(-1\) |
\(277\) | \(1\) |
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 | 8033.2.a.d | ✓ | 168 |
By twisted newform orbit | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Mult | Type |
8033.2.a.d | ✓ | 168 | 1.a | even | 1 | 1 | trivial |
Hecke kernels
This newform subspace can be constructed as the kernel of the linear operator \( T_{2}^{168} - 12 T_{2}^{167} - 188 T_{2}^{166} + 2803 T_{2}^{165} + 15629 T_{2}^{164} + \cdots + 9648337658368 \) acting on \(S_{2}^{\mathrm{new}}(\Gamma_0(8033))\).