Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [93,3,Mod(46,93)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(93, base_ring=CyclotomicField(10))
chi = DirichletCharacter(H, H._module([0, 7]))
N = Newforms(chi, 3, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("93.46");
S:= CuspForms(chi, 3);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 93 = 3 \cdot 31 \) |
Weight: | \( k \) | \(=\) | \( 3 \) |
Character orbit: | \([\chi]\) | \(=\) | 93.j (of order \(10\), degree \(4\), minimal) |
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: | no |
Analytic conductor: | \(2.53406645855\) |
Analytic rank: | \(0\) |
Dimension: | \(40\) |
Relative dimension: | \(10\) over \(\Q(\zeta_{10})\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{10}]$ |
$q$-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 | \( a_{2} \) | \( a_{3} \) | \( a_{4} \) | \( a_{5} \) | \( a_{6} \) | \( a_{7} \) | \( a_{8} \) | \( a_{9} \) | \( a_{10} \) | ||||||||||||||||||
---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
46.1 | −2.81198 | + | 2.04302i | −1.01807 | + | 1.40126i | 2.49722 | − | 7.68566i | 8.54726 | − | 6.02026i | 2.24339 | − | 6.90443i | 4.38352 | + | 13.4911i | −0.927051 | − | 2.85317i | −24.0347 | + | 17.4623i | |||
46.2 | −2.30022 | + | 1.67121i | 1.01807 | − | 1.40126i | 1.26201 | − | 3.88406i | −2.14190 | 4.92461i | 2.44257 | − | 7.51745i | 0.0737491 | + | 0.226976i | −0.927051 | − | 2.85317i | 4.92684 | − | 3.57956i | ||||
46.3 | −1.88421 | + | 1.36896i | −1.01807 | + | 1.40126i | 0.440127 | − | 1.35457i | −1.03397 | − | 4.03396i | −2.42647 | + | 7.46790i | −1.85375 | − | 5.70527i | −0.927051 | − | 2.85317i | 1.94822 | − | 1.41546i | |||
46.4 | −0.834306 | + | 0.606159i | −1.01807 | + | 1.40126i | −0.907430 | + | 2.79278i | −6.68474 | − | 1.78619i | 3.83492 | − | 11.8027i | −2.21050 | − | 6.80322i | −0.927051 | − | 2.85317i | 5.57712 | − | 4.05201i | |||
46.5 | −0.343439 | + | 0.249523i | 1.01807 | − | 1.40126i | −1.18038 | + | 3.63283i | −9.35344 | 0.735280i | −3.34669 | + | 10.3001i | −1.02582 | − | 3.15714i | −0.927051 | − | 2.85317i | 3.21234 | − | 2.33390i | ||||
46.6 | 0.506379 | − | 0.367906i | 1.01807 | − | 1.40126i | −1.11500 | + | 3.43163i | 6.13088 | − | 1.08412i | 0.632043 | − | 1.94523i | 1.47158 | + | 4.52905i | −0.927051 | − | 2.85317i | 3.10455 | − | 2.25559i | |||
46.7 | 0.722232 | − | 0.524732i | −1.01807 | + | 1.40126i | −0.989793 | + | 3.04627i | −0.251341 | 1.54625i | −2.35961 | + | 7.26213i | 1.98709 | + | 6.11563i | −0.927051 | − | 2.85317i | −0.181527 | + | 0.131887i | ||||
46.8 | 2.14291 | − | 1.55692i | −1.01807 | + | 1.40126i | 0.932010 | − | 2.86843i | 6.01190 | 4.58783i | 1.84262 | − | 5.67100i | 0.805383 | + | 2.47872i | −0.927051 | − | 2.85317i | 12.8830 | − | 9.36002i | ||||
46.9 | 2.21529 | − | 1.60950i | 1.01807 | − | 1.40126i | 1.08094 | − | 3.32680i | −3.48111 | − | 4.74279i | 2.48029 | − | 7.63354i | 0.424767 | + | 1.30730i | −0.927051 | − | 2.85317i | −7.71166 | + | 5.60285i | |||
46.10 | 2.58734 | − | 1.87981i | 1.01807 | − | 1.40126i | 1.92457 | − | 5.92321i | 2.25645 | − | 5.53932i | −4.10699 | + | 12.6400i | −2.20191 | − | 6.77679i | −0.927051 | − | 2.85317i | 5.83820 | − | 4.24170i | |||
58.1 | −1.18163 | − | 3.63669i | −1.64728 | − | 0.535233i | −8.59320 | + | 6.24332i | −0.0151265 | 6.62309i | −3.76145 | + | 2.73285i | 20.4848 | + | 14.8831i | 2.42705 | + | 1.76336i | 0.0178739 | + | 0.0550103i | ||||
58.2 | −0.923820 | − | 2.84322i | 1.64728 | + | 0.535233i | −3.99442 | + | 2.90211i | 8.90434 | − | 5.17804i | 1.59402 | − | 1.15813i | 2.26711 | + | 1.64715i | 2.42705 | + | 1.76336i | −8.22601 | − | 25.3170i | |||
58.3 | −0.481994 | − | 1.48342i | −1.64728 | − | 0.535233i | 1.26784 | − | 0.921139i | 6.42554 | 2.70159i | 0.594204 | − | 0.431714i | −7.02503 | − | 5.10399i | 2.42705 | + | 1.76336i | −3.09707 | − | 9.53180i | ||||
58.4 | −0.291155 | − | 0.896083i | −1.64728 | − | 0.535233i | 2.51787 | − | 1.82934i | −8.84927 | 1.63193i | −2.33169 | + | 1.69407i | −5.42135 | − | 3.93884i | 2.42705 | + | 1.76336i | 2.57651 | + | 7.92969i | ||||
58.5 | −0.198592 | − | 0.611203i | 1.64728 | + | 0.535233i | 2.90194 | − | 2.10838i | −4.31719 | − | 1.11311i | 8.23580 | − | 5.98366i | −3.94463 | − | 2.86594i | 2.42705 | + | 1.76336i | 0.857359 | + | 2.63868i | |||
58.6 | −0.103278 | − | 0.317856i | 1.64728 | + | 0.535233i | 3.14570 | − | 2.28549i | 1.90053 | − | 0.578875i | −2.74648 | + | 1.99543i | −2.13287 | − | 1.54962i | 2.42705 | + | 1.76336i | −0.196282 | − | 0.604094i | |||
58.7 | 0.397404 | + | 1.22308i | −1.64728 | − | 0.535233i | 1.89806 | − | 1.37902i | 2.24215 | − | 2.22746i | 3.94472 | − | 2.86601i | 6.60263 | + | 4.79709i | 2.42705 | + | 1.76336i | 0.891038 | + | 2.74233i | |||
58.8 | 0.694084 | + | 2.13617i | 1.64728 | + | 0.535233i | −0.845405 | + | 0.614223i | 2.10985 | 3.89036i | −2.29578 | + | 1.66798i | 5.36967 | + | 3.90130i | 2.42705 | + | 1.76336i | 1.46441 | + | 4.50700i | ||||
58.9 | 0.928173 | + | 2.85662i | −1.64728 | − | 0.535233i | −4.06272 | + | 2.95174i | −3.87558 | − | 5.20244i | −10.7252 | + | 7.79233i | −2.48294 | − | 1.80396i | 2.42705 | + | 1.76336i | −3.59721 | − | 11.0711i | |||
58.10 | 1.16081 | + | 3.57260i | 1.64728 | + | 0.535233i | −8.17995 | + | 5.94308i | −4.52523 | 6.50638i | 4.25581 | − | 3.09203i | −18.5715 | − | 13.4930i | 2.42705 | + | 1.76336i | −5.25293 | − | 16.1669i | ||||
See all 40 embeddings |
Inner twists
Char | Parity | Ord | Mult | Type |
---|---|---|---|---|
1.a | even | 1 | 1 | trivial |
31.f | odd | 10 | 1 | inner |
Twists
By twisting character orbit | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Mult | Type | Twist | Min | Dim |
1.a | even | 1 | 1 | trivial | 93.3.j.a | ✓ | 40 |
3.b | odd | 2 | 1 | 279.3.v.c | 40 | ||
31.f | odd | 10 | 1 | inner | 93.3.j.a | ✓ | 40 |
93.k | even | 10 | 1 | 279.3.v.c | 40 |
By twisted newform orbit | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Mult | Type |
93.3.j.a | ✓ | 40 | 1.a | even | 1 | 1 | trivial |
93.3.j.a | ✓ | 40 | 31.f | odd | 10 | 1 | inner |
279.3.v.c | 40 | 3.b | odd | 2 | 1 | ||
279.3.v.c | 40 | 93.k | even | 10 | 1 |
Hecke kernels
This newform subspace is the entire newspace \(S_{3}^{\mathrm{new}}(93, [\chi])\).